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 2 of 11.
Kavi said:
1 decade ago
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
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:
1 decade ago
I dont get the fifth line. kindly explain better.
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.
Lokmani said:
1 decade ago
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
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:
1 decade ago
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
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:
1 decade ago
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.
((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:
1 decade ago
a = 2, b = 5.
a-b = 3.
2*2 + 5*5.
4+25 = 29.
Then ab = 10.
a-b = 3.
2*2 + 5*5.
4+25 = 29.
Then ab = 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.
MANOJ K P said:
1 decade ago
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.
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:
1 decade ago
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.
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.
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