# Aptitude - Simplification - Discussion

### Discussion :: Simplification - General Questions (Q.No.4)

4.

If a - b = 3 and a2 + b2 = 29, find the value of ab.

 [A]. 10 [B]. 12 [C]. 15 [D]. 18

Explanation:

2ab = (a2 + b2) - (a - b)2

= 29 - 9 = 20 ab = 10.

 Satish said: (Sep 6, 2010) Actually (a-b)^2 = a^2 - 2ab + b^2 substitute in above formula we can get the answer.

 Kumar said: (Dec 28, 2010) It's correct.

 Sharmila said: (Mar 25, 2011) @Satish is correct this is easy.

 Rachana said: (May 25, 2011) Please explain the formula in explanation.

 Nagendramurthy said: (Jun 17, 2011) =(a2+b2)-(a-b)2 =(a2+b2)-(a2-2ab+b2) removing brackets =a2+b2-a2+2ab-b2 hence we get 2ab therefore 2ab=(a2+b2)-(a-b)2 they have given the value of a2+b2=29 and a-b=3. substituting the value 2ab= 29-(3)2 =29-3*3 =29-9 2ab=20 ab=20/2 ab=10 I think you got me.. have a nice day..

 Vishnu Dilip said: (Aug 7, 2011) Easy method Given a - b = 3 and a*a - b*b = 3, So, a = 5 and b= 2, So, ab = 5*2 = 10

 Myself said: (Aug 8, 2011) (a-b)2= a2+b2-2ab..................{eq 1} it is given that:(a-b)=3,a2+b2=29. so put it in {eq 1},we get: 3*3=29-2ab. 9=29-2ab. 2ab=29-9 2ab=20 ab=10.

 Pritam Das said: (Aug 9, 2011) (a-b)^2+2ab=29 or,(3)^2+2ab=29 or,9+2ab=29 or,2ab=20 or,ab=10

 Akash said: (Oct 22, 2011) In a2+b2=29. substract both side by 2ab.

 Sunita said: (Nov 24, 2011) Where did 9 come from? How did we arrive at 29-9?

 Kavi said: (Dec 1, 2011) a-b=3 and a2+b2=29 b=a-3 sub in above equ, a2+(a-3)2=29 a2+a2-6a+9=29 a2-3a-10=0 a=5 or -2 let we taken a=5 5^2+b2=29 25+b2=29 b=2 ab=(5)(2) ab=10

 Jay said: (Feb 24, 2012) I dont get the fifth line. kindly explain better.

 Gurpreet Singh said: (Jul 22, 2012) a-b=3 and a^2+b^2=29. Firstly a-b=3. Squaring both sides,we get (a-b)^2=3^2. a^2+b^2-2.ab=9. a^2+b^2=29 ............(1). a^2+b^2-2.ab=9.........(2). Subtract (2) from (1).. a^2+b^2-[a^2+b^2-2.ab] = 29-9. a^2 + b^2 - a^2 - b^2 + 2.ab = 29-9. 2ab=20. ab =20/2 = 10.

 Lokmani said: (Oct 4, 2012) a-b=3 a^2+b^2=29 (a-b)^2=a^2+b^2-2ab (3)^2=29-2ab 9=29-2ab 2ab=29-9 2ab=20 ab=20/2 ab=10

 Satheesh M said: (Dec 22, 2012) a^2 + b^2 = 29 a^2 + b^2 = 5x5 + 2x2 a^2 + b^2 = 25+4 so that a = 5 and b = 2 then ab = 5x2 => 10

 Deep Goel said: (Jan 20, 2013) a+b=3 a-b=1 then ab=? ((a+b)^2-(a-b)^2)/4=ab :^2=squaring. (3^2-1^2)/4= ab. (9-1)/4=ab. 8/4=2=ab.

 Anita said: (Aug 15, 2013) a = 2, b = 5. a-b = 3. 2*2 + 5*5. 4+25 = 29. Then ab = 10.

 Boopathi said: (Aug 26, 2013) A-B = 3. A = 3+B. WE KNOW THAT, A^2+B^2 = 29. (3+B) ^2+B^2 = 29. 9+B^2+6B+B^2 = 29. 2B^2+6B-20 = 0. B^2+3B-10 = 0. SOLVE THIS EQN. B = 2 & B = -5. THEN TAKE +VALVE B = 2. WE KNOW THAT A-B = 3. SO A-2 = 3. A = 5. KNOW FIND. AB = 2*5 = 10.

 Manoj K P said: (Sep 22, 2013) VERY SIMPLE. A-B = 3. SQUARE IT BOTH SIDE. (A-B) ^2 = (3*3). A^2+B^2-2AB = 9. 2AB = A^2+B^2-9. WE HAVE A^2+B^2 = 29 APPLY THIS. 2AB = 29-9. 2AB = 20. AB = 20/2. AB = 10.

 Vamshi said: (Apr 12, 2014) A-B = 3. A^2+B^2 = 29. Squaring on both sides. (A-B) ^2 = 3^2. A^2+B^2-2AB = 9. 29-2AB =9. 20 = 2AB. AB = 10.

 Bhavana said: (May 14, 2014) I didn't get the fifth line. Can you explain it.

 Krishna said: (Sep 18, 2014) a^2+b^2=(a-b)(a-b)+2ab. Now putting the value of (a-b)we get that 9+2ab=29, 2ab=20, ab=10.

 Krishna said: (Sep 18, 2014) a2+b2=(a-b)(a-b)+2ab hota hi 3*3+2ab=29,2ab=20,ab=10

 Suganya said: (Nov 5, 2014) Sathish said correct solution and take a time shortly to solve the problem.

 Ram said: (Nov 13, 2014) (a+b)^2-(a-b)^2 = 4ab.

 Arshiya said: (Nov 25, 2014) If (a-b) = 7 ab = 9, then find the value of (a2+b2)?

 Prasad said: (May 13, 2015) (a-b)^2 = a^2+b^2-2ab. Then 2ab = (a^2+b^2)-(a-b)^2. 2ab = 29-(3)^2. 2ab = 20. ab = 10.

 Manjunatha Dv said: (May 24, 2015) a-b = 3. 5-2 = 3. a^2+b^2 = 29. 5^2+2^2 = 29. Answer = 5*2 = 29.

 Harisha said: (Sep 23, 2015) Solve the problem if a+1/a-2=4. Find the value of (a-2)^2+(1/a-2)^2?

 Jisha said: (Feb 19, 2016) @Harisha can you explain your question?

 Smruti Ranjan said: (Mar 2, 2016) If a2 - b2 = 37, then a2 + b2 = ? Please explain?

 Saad said: (Apr 1, 2016) If a2 - b2 = 30 and a - b = 5, then find the value of ab?

 Hepinder Happy said: (Apr 19, 2016) @Saad. a^2 - b^2 = (a+b)(a-b) we have given a^2 - b^2 = 30 and a - b= 5. Then (a + b)(a - b) = 30. a + b = 30/(a -b). a + b = 30/5. a + b = 6 Solving 1 & 2 we get, 2a = 11. a = 11/2 then ab =11/4 --> Answer.

 Amit said: (Jun 10, 2016) It's so easy Easy method. Given. a - b = 3 and a * a - b * b = 3, So, a = 5 and b = 2. Then, ab = 5 * 2 = 10.

 Antara Chatterjee said: (Aug 10, 2016) a2 + b 2= 52,and a - b = 2. Then ab? Anyone solve this problem.

 Rushah said: (Aug 28, 2016) @Antara. It's very easy. Remove brackets and multiply you got 2ab.

 Raj said: (Sep 28, 2016) If a + 1/a = 4, then a^2 + 1/a^2 = ?

 Gh Mustafa said: (Oct 15, 2016) How can solve this a^2 + b^2 = 16 and (a - b)^2 = 4 then ab is equal to?

 John Audu said: (Oct 21, 2016) @Gh Mustafa If a ^2+b^2=16 and (a - b)^2 = 4 = (a2 + b2) = 16 (a2 - b2) = 4. Clear thé bracket = a + b = 16, a - b = 4. Since we are finding ab = a + b = 16/4 = 4. So, a + b = ab.ab = 4.

 Nagaraj said: (Nov 19, 2016) a^2+b^2 = 29, a = 5, b = 2. 5^2 + 2^2 = 29. Thank you.

 Neeraj Kashyap said: (Nov 22, 2016) Please solve the following with explanation: 1. (a + b) (a - b) + (2a + b) (2a - 3b). 2. (x - y)(2x + y) - (x + y)(2x - y). 3. (x + 6){5x - 3(x - 2)} 4. 7x - 3{x - 2x(x - 4)}

 Anil Malav said: (Nov 28, 2016) (a^2 + b^2)^1/2 = 613 then find the value of a+b. Solve and find the answer.

 Rah1 said: (Dec 6, 2016) Awesome answer @Ram.

 Francium said: (Dec 7, 2016) Guys, please solve this for me a2 + b2 = 36 and an=7 find the value of (a+b)2.

 Gyanika said: (Jan 4, 2017) Can somebody please solve this question. a - b = 1, 2a + 20 = b. Then a, b is?

 Sonali said: (Jan 8, 2017) a-b = 3, a2+b2=29, ab =? (a-b)2 = a2+b2-2ab 2ab = (a2+b2)-(a-b)2 ab = 29-9/2 = 20/2 = 10 Ans.

 Tanim Ehsan said: (Jan 8, 2017) If a + b = 13 and ab = 3 then (a+2b)^2-5b^2 = ? Simplify the solution.

 Bonjor said: (Jan 10, 2017) I would be grateful if anyone answers this question. If a-b=4 and ab=60 then find the value of a+b. I found that the answer is + or - 16 what is + or -? Please tell me.

 Harsh Singh said: (Jan 24, 2017) Yes @Bonjor. (a+b)2 = (a-b)2+4ab, (a+b)2 = 256, a+b = +-16. +-16 is the answer.

 Venkat@Rockzzzz said: (Jan 27, 2017) (a-b)^2 = a^2+b^2-2ab. 2ab = a^2+b^2-(a-b)^2, = 29-3^2, = 29-9, 2ab = 20. ab =10.

 Venkat@Rockzzzz said: (Jan 27, 2017) (a-b)^2 = a^2+b^2-2ab. 2ab = a^2+b^2-(a-b)^2, = 29-3^2, = 29-9, 2ab = 20. ab =10.

 Yaswanth Chinni said: (Jan 28, 2017) 2ab = (a2 + b2) - (a - b)2. = 29 - 9 = 20, ab = 10.

 Sandilya said: (Jan 28, 2017) Yes @Harsh Singh. (a+b)2 = (a-b)2+4ab, (a+b)2 = 256, a+b = +-16. +-16 is the answer.

 Mangesh said: (Feb 24, 2017) Please give the answer of (a-b) =4 ab=52.25 then a^2 * b^2 = ?

 Rowwah said: (Feb 26, 2017) (a-b)^2 = a^2 + b^2 - 2ab, (3)^2 = 29 - 2ab, 2ab = 29 - 9 = 20 ab = 10.

 Pramod Kumar said: (Mar 3, 2017) Simple solution: a - b = 3 ---> (1); a^2+b^2 = 29 ---> (2); Then we add 2ab and subtract 2ab in equation 2; a^2+b^2 - 2ab+2ab = 29; Then we get, (a - b)^2+2ab = 29. 2ab = 29 - (a - b)^2. Then we put value of a - b=3; 2ab=29 - 9; 2ab = 20; ab = 10.

 Gween said: (Mar 4, 2017) Please give me the answer of this? I don't get it. What are the values of a and b in the equation 2a+3b = 5 if the sum of a and b is 4?

 Sachin Kumar said: (Mar 14, 2017) If a^2+b^2 = (a+b)^2. And (a+b)^2 = a^2+b^2+2ab. It means a^2+b^2 = a^2+b^2+2ab. But How Could it Possible, Please somebody tell me what actually is it?

 Sachin Kumar said: (Mar 14, 2017) @Gween. a + b = 4 means a=4-b. Put this value in the equation 5= 2(4-b)+3b, 5= 8-2b+3b, 5-8 = -2b+3b, -3= b. Put the value of b in the equation and u will get the value of a. Thats it!

 Sourav Das said: (Mar 19, 2017) If a+b = √5 & a-b= √3 than find the value of a2 + b2.

 Mba P said: (Mar 21, 2017) If a * b = 3a - 2b. Find (4*2)*7 WHAT DOES THIS MEAN? EXPLAIN ME PLEASE.

 Abid said: (Apr 2, 2017) Please solve this problem. If √a + √b- √c = 0 Then find (a+b-c)^2.

 Akhthar Khilji said: (Apr 23, 2017) Please verify this, is it right or wrong? My method is As a^2+b^2=29 (a+b)(a-b)=29----> 1 Given a-b=3----> 2 Put 2 in 1 (a+b)3=29----> 3 (a+b)=29/3 (a+b)=9.6666----> 4 Putting 4 in 3 9.6666 * 3=29. Thus it satisfies the equation, 29 = 29.

 Ashif Rahim said: (May 10, 2017) Answer : A=5 & B=2. AB = 10.

 Govind said: (May 17, 2017) If a+b+c=0 then {(a^2 + b^2 + c^2)^2} / {(a^2 * b^2) + (b^2 * c^2) + (c^2 * a^2)}.

 Rishabh said: (May 21, 2017) 3^a, 5^-b, 15^c find 1/a-1/b-1/c. Please solve this.

 Harshit Shrivastava said: (Jun 2, 2017) Please solve my question. If a + b = -5 find the value of a^3+b^3+125.

 Raman Deep said: (Jun 16, 2017) If (2-a+b, b)=(6, 2), then find the value of a and b. Can anyone solve this?

 Nripendra said: (Jun 20, 2017) If a2+b2=25 and ab=12 then find the value of a2-b2? Can anyone tell me?

 Deepa Shrestha said: (Jun 25, 2017) If a/b=2/3 then 3a + 5b / 3a - 5b =? Solve this problem?

 Farman said: (Jul 31, 2017) Let's look it if a2+b2=25 and a-b=3 ab=? 25-(3)^2=16 then 16/2 =8.

 Sanjay Rajput said: (Aug 2, 2017) a+b/a+b-a+3b/a+b+a+5b/a+b to 15th term sum of numbers.

 Adwait Phadke said: (Aug 16, 2017) @Deepa. a/b=2/3 so 3a=2b Substituting 3a=2b in eqn 3a+5b/3a-5b =2b+5b/2b-5b =7b/-3b. =-7/3.

 Samuel said: (Aug 18, 2017) If a=? and b=4. Find the value of 3a+b. Can anyone solve this?

 Akash said: (Aug 19, 2017) Would anyone, please solve it. X/y+y/x=8,then x^4/y^4+y^4/X^4=?

 Abhijeet said: (Aug 19, 2017) It'snot an equation. We take the equation: 3a+b 3a+4= ?

 Kanishka said: (Aug 21, 2017) If x+1/x=3, then find the value of x^3+1/x^3.

 Arpitha Sharma said: (Aug 28, 2017) Here, (2a-3b) (4a^+6ab+9b^) +27b^3.

 Bubhiramsingh said: (Sep 4, 2017) If log ab=log(a+b) then proved(a+b)2-(a-b)2 = 4(a+b).

 Chirag said: (Sep 14, 2017) I didn't understand. Please tell me.

 Imane said: (Sep 15, 2017) What about if its: find the value of a and b and we have just a+b=2 and ab=-5?

 Shanto said: (Nov 12, 2017) a/b=4a, 2b=12, than what is the value of a? or is it wrong?

 Rushabh said: (Nov 16, 2017) log(a+b/2) = 1/2(loga+logb) so prove that a^2+b^2=4ab is that possible.

 Karthi said: (Dec 14, 2017) 2ab = (a2 + b2) - (a - b)2. => a - b = 3 (a - b)2 (3)2 =9 => a2 + b2 = 29 (a2 + b2) =29. Therefore 29-9 = 20, 2ab = 20, ab =10.

 Dharmender Meena said: (Dec 20, 2017) (a-b)2=a2+b2-2ab. 9=29-2ab, 2ab=29-9, ab=20/2, ab=10.

 Dinesh said: (Dec 30, 2017) Let us assume a=5, b=2. a^+b^=25+4=29. a-b =5-2=3. So ab=5*2=10.

 Bahisht said: (Jan 17, 2018) Your Method is easy @Satish.

 Mohamed said: (Jan 27, 2018) Can anyone explain this to me I found it confused it. If (a+b) / (a-b) +3/7, what is the value a/b?

 Shilpi said: (Feb 18, 2018) I can't understand it, please explain me.

 Laxmi said: (Mar 24, 2018) What will be the answer, if a+b=5, a^2 + b^2 =30, Find b. Anyone olve it.

 Ashraf said: (Jun 3, 2018) I can't understand. Please explain me.

 Sivakumar said: (Oct 6, 2018) Please explain the formula clearly.

 Prince said: (Oct 7, 2018) We can write a^2+b^2=(a-b)^2+2ab. When we solve (a-b)^2+2ab we will get a^2+b^2. Now put the value of (a-b) and a^2+b^2 in the equation a^2+b^2=(a-b)^2+2ab. Ans is - 10.

 Saritha said: (Oct 10, 2018) it is given that (a-b)=3 and a^2+b^2=29. So, (a-b)^2=a^2+b^2-2ab. {substitute a-b=3 and a^2+b^2=29} =>3^2=29-2ab, =>2ab=20, => ab=10.

 Jan said: (Oct 30, 2018) (a-b)^2 = a^2+b^2-2ab. (3)^2 = 29-2ab, 9 = 29-2ab, 9-29 = -2ab, -20 = -2ab, 10 = ab.

 Jan said: (Oct 30, 2018) (a-b)^2 = a^2+b^2-2ab. (3)^2 = 29-2ab, 9 = 29-2ab, 9-29 = -2ab, -20 = -2ab, 10 = ab.

 Sakshi said: (Feb 9, 2019) Thanks @Satish.

 Alex said: (Sep 13, 2019) Thanks for explaining @Dharmender Meena.

 Sai said: (Feb 22, 2020) Can anyone explain this once again clearly?

 Sunil said: (Mar 28, 2020) Simply tack, a-b=3 n square on both side . A square + b square - 2AB=3 square----------> (1). 29-2AB=9 HENCE 2AB=29-9> 2AB=20 SO AB=10.

 Varshith said: (Apr 8, 2020) Thanks @Janu.

 Avi said: (Jan 20, 2021) Thanks @Satish.