Question

if x-1/x=5 then find the value of x^3-1/x^3
Pls guys its very urgent pls answer fast​

Answer 1

Given:

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x – 1/x = 5

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To find:

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x$^{3}$ – 1/x$^{3}$

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Solution:

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x – 1/x = 5 (given)

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By squaring both sides, we get

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(x – 1/x)$^{2}$ = 5$^{2}$

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$\implies$ x$^{2}$ + 1/x$^{2}$ = 2(x)(1/x) = 25

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$\implies$ x$^{2}$ + 1/x$^{2}$ – 2 = 25

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$\implies$ x$^{2}$ + 1/x$^{2}$ = 25 + 2

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$\implies$ x$^{2}$ + 1/x$^{2}$ = 27

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So, now we have to find x$^{3}$ – 1/x$^{3}$

Using identity of a$^{3}$ – b$^{3}$ = (a + b) (a$^{2}$ + b$^{2}$ + ab)

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$\implies$ x$^{3}$ – 1/x$^{3}$ = (x – 1/x) [(x)$^{2}$ + (1/x)$^{2}$ + x(1/x)]

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= 5 (27 + 1)

= 5 × 28

= 140

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Hence, 140 is the required solution.