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Question
If x2 + y2 = 29 and xy = 2, find the value of x - y.
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Solution
We have:
\[\left( x - y \right)^2 = x^2 - 2xy + y^2 \]
\[ \Rightarrow \left( x - y \right) = \pm \sqrt{x^2 - 2xy + y^2}\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 2 \times 2} (\because x^2 + y^2 = 29 \text { and } xy = 2)\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{29 - 4}\]
\[ \Rightarrow \left( x + y \right) = \pm \sqrt{25}\]
\[ \Rightarrow \left( x + y \right) = \pm 5\]
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