Question

if x+1/x =13 find xcube +1/xcube​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given,

$\mathsf{x + \frac{1}{x} = 13}$

To find:

$\mathsf{x {}^{3} + \frac{1}{x {}^{3} } }$

Of the form,

(a+b)³=a³+b³+3ab(a+b)

Here,

$\sf{a = x \: \: and \: \: b = \frac{1}{x} }$

Putting the values

$\mathsf{(x + \frac{1}{x}) {}^{3} = x {}^{3} + \frac{1}{x {}^{3} } + 3(x + \frac{1}{x}) } \\ \\ \implies \: \sf{13 {}^{3} =x {}^{3} + \frac{1}{x {}^{3}} + 3(13) \: } \\ \\ \implies \: \sf{x {}^{3} + \frac{1}{x {}^{3} } = 2197 - 39 } \\ \\ \implies \: \sf{x {}^{3} + \frac{1}{x {}^{3} \: } = 2158 }$