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

Answer: Option A

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.

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