Question

کل
If x + y =9 and xy = 18, find the value of x³+1/x³​

Answer 1

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$x + y = 9$

$xy = 18$

Therefore,

${x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x} )}^{3} - 3 \times x \times \frac{1}{x} (x + \frac{1}{x} )$

$\implies {x}^{3} + \frac{1}{ {x}^{3} } = {9}^{3} - 3 \times 9$

$\implies {x}^{3} + \frac{1}{ {x}^{3} } = 729 - 27$

$\implies {x}^{3} + \frac{1}{ {x}^{3} } = 702$

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