porvakanti wrote:
What is the value of x^2 – y^2?
(1) x + y = 66
(2) xy = 9
OA:E
What is the value of \(x^2 – y^2\) or \((x-y)(x+y)\)?
(1) \(x + y = 66\)
We are given the value of \(x + y\), and not given the value of \(x-y\)
So Statement 1 alone is not sufficient.
(2) \(xy = 9\)
The product of \(xy\) is given but we cannot find either individual value of \(x\) and \(y\) or value of expression of \(x^2 – y^2\) or \((x-y)(x+y)\)
So Statement 2 alone is not sufficient.
Combining 1 and 2, we get
\(x + y = 66\)
\((x-y)^2 =(x + y)^2-4xy\)
\((x-y)^2=(66)^2-4*9=(66)^2-(6)^2 =(66+6)(66-6)=72*60=2^1*3^1*5^1*12^2\)
\(x-y = ±12\sqrt{30}\)
So Expression \(x^2 – y^2\) can have 2 values : \(12*66*\sqrt{30}\) or \(-12*66*\sqrt{30}\)
Combining (1) and (2) will also not give unique value of expression \(x^2 – y^2\)