Aptitude - Simplification - Discussion
Discussion Forum : Simplification - General Questions (Q.No. 4)
4.
If a - b = 3 and a2 + b2 = 29, find the value of ab.
Answer: Option
Explanation:
2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
Discussion:
107 comments Page 1 of 11.
Nagendramurthy said:
1 decade ago
=(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..
=(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..
(1)
Gurpreet singh said:
1 decade ago
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.
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.
BOOPATHI said:
1 decade ago
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.
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.
Pramod kumar said:
8 years ago
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.
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.
Akhthar khilji said:
8 years ago
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.
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.
Heyrobin said:
4 years ago
It's easy.
Use the formula!
(a+b)2 = a2 + b2 + 2ab.
(a-b)2 = a2+b2 - 2ab.
I am choosing (a-b)2 formula as that is in my question a-b = 3.
(a-b)2 = (a2+b2) - 2ab.
(3)2 = (29) - 2ab.
9 = 29 - 2ab.
2ab= 29-9.
ab= 20/2.
ans = 10.
Use the formula!
(a+b)2 = a2 + b2 + 2ab.
(a-b)2 = a2+b2 - 2ab.
I am choosing (a-b)2 formula as that is in my question a-b = 3.
(a-b)2 = (a2+b2) - 2ab.
(3)2 = (29) - 2ab.
9 = 29 - 2ab.
2ab= 29-9.
ab= 20/2.
ans = 10.
(31)
Tulasi said:
4 years ago
a-b=3 ----> (i)
a^2+b^2=29 ----> (ii).
Eqn(i) squaring on both sides
(a-b)^2 = 3^2.
a^2+b^2-2ab=9.
a^2+b^2=9+2ab ----> (iii)
substitute eqn(iii) in eqn(ii).
a^2+b^ 2= 29,
9+2ab = 29,
2ab = 29-9,
2ab = 20,
ab = 10.
a^2+b^2=29 ----> (ii).
Eqn(i) squaring on both sides
(a-b)^2 = 3^2.
a^2+b^2-2ab=9.
a^2+b^2=9+2ab ----> (iii)
substitute eqn(iii) in eqn(ii).
a^2+b^ 2= 29,
9+2ab = 29,
2ab = 29-9,
2ab = 20,
ab = 10.
(9)
Hepinder happy said:
9 years ago
@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.
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.
GyaniAdmy said:
3 years ago
a-b = 3.
a^2+b^2 = 29.
Let's Get The Answer In (a-b)^2 Formula/Format
(a-b)^2=a^2+b^2-2ab
=>3^2 = 29 - 2ab
=>9 = 29 - 2ab
=>2ab = 29 - 9
=>2ab = 20.
Therefore, ab=10.
Wasn't It Easy?
a^2+b^2 = 29.
Let's Get The Answer In (a-b)^2 Formula/Format
(a-b)^2=a^2+b^2-2ab
=>3^2 = 29 - 2ab
=>9 = 29 - 2ab
=>2ab = 29 - 9
=>2ab = 20.
Therefore, ab=10.
Wasn't It Easy?
(105)
John audu said:
9 years ago
@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.
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.
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