Question

If x²+1/x²= 7 find the value of x3+ 1/x3
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Answer 1

$\huge \bf \: Answer$

$\bf \: \bigg(x + \frac{1}{x} \bigg)^{2}$

$= > \bf {x}^{2} + \frac{1}{ {x}^{2} } \: + 2$

$= > \bf \bigg( \frac {x + 1}{x} \bigg)^{2} = 9$

$\ = > \bf \: x \: + \frac{1}{x} = 3$

$\bf \: now$

$\bf \: Now ,$

$\bf \bigg( \frac{x + 1}{x} \bigg) ^{3}$

$= > \bf \: {x}^{3} + \frac{1} { {x}^{3} } \: + 3 \bigg(x + \frac{1}{x} \bigg)$

$= > \bf \: 27 \: \: = \: {x}^{3} \: + \: \frac{1}{ { x }^{3} } \: + 9$

$\bf \: Or,$

$\bf \: {x}^{3} + \frac{1}{ {x}^{3} }$

$= > \bf \: 27 \: - \: 9 \: = 18$

Answer 2

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