Question

If x − y = 7 and xy = 9, find the value of x² + y²

Answer 1

We have:

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

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

\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\]      (\[\because\]  \[x - y = 7 \text { and } xy = 9\])

\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\]

\[ \Rightarrow x^2 + y^2 = 49 + 18\]

\[ \Rightarrow x^2 + y^2 = 67\]