Question

(x+y=12) and xy = 14,find the value of (x²+y²)

Answer 1

Hey dear here is your answer!!!!!!!

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$given \: xy = 14 \: and \: x + y = 12 \\ \\ we \: know \: that \: \\ \\ x ^{2} + y ^{2} + 2xy = (x + y {)}^{2} \\ x ^{2} + {y}^{2} = (x + y)^{2} - 2xy \\ substitue \: values \: \\ {x}^{2} + {y}^{2} = 12 ^{2} - 2 \times 14 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 144 - 28 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 116$
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