Question

❤${\bold{\purple{\small{Hello Frndz}}}}$❤
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Given:
${x}^{2} + \frac{1}{ {x}^{2} } = 10$
Find:
${x}^{3} + 3x + \frac{3}{x} + \frac{1}{ {x}^{3} }$
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Answer 1

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$\bold{1.}$

${x}^{2} + \frac{1}{ {x}^{2} } = 10$

$(x + \frac{1}{x} )^{2} - 2 = 10$

$(x + \frac{1}{x} ) ^{2} = 10 + 2$

$(x + \frac{1}{x} )^{2} = 12$

$x + \frac{1}{x} = ±2 \sqrt{3}$

$(x)^{3} + ( \frac{1}{x} )^{3} + 3 \times (x)^{2} \times \frac{1}{x} + 3 \times x \times \frac{1}{x^{2} }$

$(x + \frac{1}{x} )^{3} = (2 \sqrt{3} ) ^{3}$

$= 8 \times 3 \sqrt{3}$

$= ±24 \sqrt{3}$

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Answer 2

Hope it helps uhh✌✌✌