Question

If x² + y² = 29 and xy = 2, find the value of x - y.

Answer 1

 We have:

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

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

\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 2 \times 2} (\because x^2 + y^2 = 29 \text { and } xy = 2)\]

\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 4}\]

\[ \Rightarrow \left( x + y \right) = \pm \sqrt{25}\]

\[ \Rightarrow \left( x + y \right) = \pm 5\]