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Question
If x − y = 7 and xy = 9, find the value of x2 + y2
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Solution
We have:
\[\left( x - y \right)^2 = x^2 - 2xy + y^2 \]
\[ \Rightarrow x^2 + y^2 = \left( x - y \right)^2 + 2xy\]
\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\] (\[\because\] \[x - y = 7 \text { and } xy = 9\])
\[\Rightarrow x^2 + y^2 = 7^2 + 2 \times 9\]
\[ \Rightarrow x^2 + y^2 = 49 + 18\]
\[ \Rightarrow x^2 + y^2 = 67\]
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