If $x - y = 7$ and $x y = 9$ , find the value of $(x^{2} + y^{2})$

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Solution

$x - y = 7$
Squaring both sides,
$(x - y)^{2} = (7)^{2} \Rightarrow x^{2} + y^{2} - 2 x y = 49 \Rightarrow x^{2} + y^{2} - 2 \times 9 = 49 \Rightarrow x^{2} + y^{2} - 2 \times 9 = 49 \Rightarrow x^{2} + y^{2} - 18 = 49 \Rightarrow x^{2} + y^{2} = 49 + 18 = 67 ∴ x^{2} + y^{2} = 67$

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