Question:
If x and y are real numbers such that x2 + (x-2y-1)2 = 4y(x+y), here the value x-2y is?
If x and y are real numbers such that x2 + (x-2y-1)2 = 4y(x+y), here the value x-2y is?
Updated On: Jan 12, 2026
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The Correct Option is A
Solution and Explanation
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.
\(x - 2y - 1 = 0 \)
\(⇒ x - 2y = 1\)
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