Question

If x and y are real numbers such that x2 + (x-2y-1)2 = 4y(x+y), here the value x-2y is?

• A. 1
• B. 2
• C. 0
• D. -1

Answer 1

Answer: (A)

1

Answer 2

We have,
$x ^2 +(x−2y−1) ^2 =−4y(x+y)$
$⇒ x^ 2 +4xy+4y^ 2 +(x−2y−1)^ 2 =0$
$⇒ (x+2y) ^2 +(x−2y−1) ^2 =0$
Since squares cannot be negative, all of the square terms in the equation must be zero for the L.H.S. to be 0.
$x - 2y - 1 = 0$
$⇒ x - 2y = 1$