Question

x2+1/x2=34, find x3-1/x3? ​

Answer 1

$The \: answer \: is \: = = > {x}^{3} - \frac{1}{ {x}^{3} } = 234$

Step-by-step explanation:

Given:-

• ${x}^{2} + \frac{1}{ {x}^{2} }$

To Find:-

• ${x}^{3} - \frac{1}{ {x}^{3} }$

$\huge{{{ \color{magenta}{ \mathfrak{ ★solution :}}}}}$

$Here \: we \: use \: the \: identity \: of \: \: {(a - b)}^{2} \: we \: have \\ \\ = = > \: \: \: {(x - \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} \\ \\ = = > \: \: \: {(x - \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ = = > \: \: \: Cut \: x \: with \: x \: we \: have\\ \\ = = > \: \: \: {(x - \frac{1}{x}) }^{2} =34 + 2 \\ \\ = = > \: \: \: {(x - \frac{1}{x}) }^{2} =36 \\ \\ Taking \: square \: root \: on \: both \: sides \\ \\ = = > \: \: \: \sqrt{{(x - \frac{1}{x}) }^{2} } = \sqrt{36} \\ \\ = = > \: \: \: x - \frac{1}{x} = 6 \: \: \: - - - - > equation \: (1)\\ \\ Now \: cubing \: both \: sides \\ \\ = = > \: {(x - \frac{1}{x}) }^{3} = {6}^{3} \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) = 216 \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } - 3(x - \frac{1}{x} ) = 216 \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 6 = 216 \: \: \: \: from \: (1) \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } - 18 = 216 \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } = 216 + 18 \\ \\ = = > \: \: \: {x}^{3} - \frac{1}{ {x}^{3} } = 234 \\ \\ This \: is \: the \: required \: answer$

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