Question

Given that x-y = 8 xy =5 find the value of x²+y²

Answer 1

Given,

$\implies$ x-y = 8 xy =5

$\implies$ Apply (x - y)² = x² + y² - 2xy

$\implies$ Put the given values...

$\implies$ 8² = x² + y² -2(5)

$\implies$ x² + y² = 64 + 10

$\implies$ x² + y² = 74

$\imploes$ Answer is $\boxed{\textbf{74}}$

Answer 2

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {8}^{2} = {x}^{2} + {y}^{2} - (2 \times 5 ) \\ 64 = {x}^{2} + {y}^{2} - 10 \\ {x}^{2} + {y}^{2} = 64 +10 = 74$
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