Question : If $x=1-y$ and $x^2=2-y^2$, then what is the value of $xy$?
Option 1: $1$
Option 2: $2$
Option 3: $-\frac{1}{2}$
Option 4: $–1$
Answer (1)
14th Jan, 2024
Correct Answer: $-\frac{1}{2}$
Solution :
Given: $x = 1-y$
⇒ $x+y = 1$
Squaring both sides, we get,
⇒ $x^2+y^2+2xy=1$
Using $x^2 = 2-y^2$
⇒ $2-y^2+y^2+2xy=1$
⇒ $2+2xy =1$
$\therefore xy = -\frac{1}{2}$
Hence, the correct answer is $-\frac{1}{2}$.
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