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in Algebraic Expressions by (38.0k points)
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If x+y = 4 and xy = 2, find the value of x2+y2

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Best answer

Given that,

x + y = 4 and xy = 2

We take the equation: x + y = 4 and on squaring both sides, we get

(x + y)2 = 42

x2 + y2 + 2xy = 16

x2 + y2 + 2(2) = 16 (Because xy = 2 is given)

x2 + y2 + 4 = 16

x2 + y2 = 16 – 4

x2 + y2 = 12

Therefore, the value of x2 + y2 is 12

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