If x=3-y and x^2=5-y^2 , then find the value of (xy)^2+3 .

The correct answer is Option (3) → 7

The two conditions give the sum \(x+y\) and the sum of squares \(x^2+y^2\). The product comes from \((x+y)^2=x^2+y^2+2xy\).

• \(x+y=3\) and \(x^2+y^2=5\)

• \(3^2=5+2xy\), so \(2xy=4\) and \(xy=2\)

• \((xy)^2=4\)

• \((xy)^2+3=4+3=7\)