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

The Correct Option is A

Given the equation,
\(x ^2 +(x−2y−1) ^2 =−4y(x+y) \)
\(⇒ x^ 2 +4xy+4y^ 2 +(x−2y−1)^ 2 =0\)
\(⇒ (x+2y) ^2 +(x−2y−1) ^2 =0\)
As squares of real numbers are non-negative, the sum of two squares equals zero if and only if each square term is zero.
\(x - 2y - 1 = 0 \)
\(⇒ x - 2y = 1\)