Question

If x-1/x=3, find the value of x^3-1/x^3​

Answer 1

Answer: 36

Step-by-step explanation:

x - 1/x = 3

Since we know that,

( a - b )³ = a³ - b³ - 3ab( a - b )

Similarly,

(x - 1/x)³ = x³ - 1/x³ - 3(x)(1/x) x - 1/x)

By substituting values we get,

3³ = x³ - 1/x³ - 3(3)

27 = x³ - 1/x³ - 9

27 + 9 = x³ - 1/x³

36 = x³ - 1/x³

Answer 2

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Solution:-

Given :-

$\frac{x - 1}{x} = 3$

We know that :-

(a - b) = a^3 - b^3 - 3ab ( a - b)

So,

Cubing on both sides. We get,

$= > { (x - \frac{ 1}{x} )}^{3} = {x}^{3} - { \frac{1}{x} }^{3} - 3x \: ( \frac{1}{x} ) \: (x - \frac{1}{x} ) \\ \\ = > {3}^{3} = {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 3 \\ \\ = > 27 = {x}^{3} - \frac{1}{ {x}^{3} } - 9 \\ \\ = > {x}^{3} - \frac{1}{ {x}^{3} } = 36.$

Hence,

${x}^{3} - \frac{1}{ {x}^{3} } = 36$