Question

Solve :-
$\large \sf \: \frac{x - 1}{x} = 5 \: \: then \: \: \frac{x {}^{3} - 1}{ {x}^{3} }$

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Answer 1

Question :-

$\large \sf \: \frac{x - 1}{x}$ = 5 then $\large \sf\frac{x {}^{3} - 1}{ {x}^{3} }$

Solution :-

1st Equation :-

$\large \sf \frac{x - 1}{x}$ = 5

x - 1 = 5x

x - 5x = 1

-4x = 1

-x = $\large \sf \frac{1}{4}$

2nd Equation :-

$\large \sf\frac{ {x}^{3} - 1 }{ {x}^{3} }$

x³ - 1 = x³

x³ - x³ = 1

= 1

Thank You*

Answer 2

Answer:-

Given:-

(x - 1)/x = 5

⟹ (x/x) - (1/x) = 5

⟹ 1 - 1/x = 5

⟹ 1 - 5 = 1/x

⟹ - 4 = 1/x

Cubing both sides we get;

⟹ (- 4)³ = (1/x)³

⟹ - 64 = 1/x³

Now;

We have to find the value of:

⟹ (x³ - 1)/x³

⟹ x³/x³ - 1/x³

Substitute the value of 1/x³

⟹ 1 - ( - 64)

⟹ 1 + 64

⟹ 65

∴ The value of (x³ - 1)/x³ is 65.