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 3 of 11.
Rachana said:
1 decade ago
Please explain the formula in explanation.
Vishnu dilip said:
1 decade ago
Easy method
Given
a - b = 3 and a*a - b*b = 3,
So,
a = 5 and b= 2,
So,
ab = 5*2 = 10
Given
a - b = 3 and a*a - b*b = 3,
So,
a = 5 and b= 2,
So,
ab = 5*2 = 10
Myself said:
1 decade ago
(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.
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:
1 decade ago
(a-b)^2+2ab=29
or,(3)^2+2ab=29
or,9+2ab=29
or,2ab=20
or,ab=10
or,(3)^2+2ab=29
or,9+2ab=29
or,2ab=20
or,ab=10
Akash said:
1 decade ago
In a2+b2=29.
substract both side by 2ab.
substract both side by 2ab.
Sunita said:
1 decade ago
Where did 9 come from?
How did we arrive at 29-9?
How did we arrive at 29-9?
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
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