Question

If x + y = 4 and xy = 2, find the value of x² + y²

Answer 1

We have:

\[\left( x + y \right)^2 = x^2 + 2xy + y^2 \]

\[ \Rightarrow x^2 + y^2 = \left( x + y \right)^2 - 2xy\]

\[\Rightarrow x^2 + y^2 = 4^2 - 2 \times 2\]    (\[\because\] \[x + y = 4 \text { and } xy = 2\])

\[\Rightarrow x^2 + y^2 = 16 - 4\]

\[ \Rightarrow x^2 + y^2 = 12\]