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Question
If x + y = 4 and xy = 2, find the value of x2 + y2
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Solution
We have:
\[\left( x + y \right)^2 = x^2 + 2xy + y^2 \]
\[ \Rightarrow x^2 + y^2 = \left( x + y \right)^2 - 2xy\]
\[\Rightarrow x^2 + y^2 = 4^2 - 2 \times 2\] (\[\because\] \[x + y = 4 \text { and } xy = 2\])
\[\Rightarrow x^2 + y^2 = 16 - 4\]
\[ \Rightarrow x^2 + y^2 = 12\]
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