Step-by-step explanation:

Given:

x minus one by x is equal to 5

To find:

Find the value of x cube minus one by x cube

Solution:

From given, we have,

x minus one by x is equal to 5

x - 1/x = 5

we use the formula,

(a - b)³ = a³ - b³ - 3ab (a - b)

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

(x - 1/x)³ = x³ - 1/x³ - 3 (x - 1/x)

using the given value, we have,

5³ = x³ - 1/x³ - 3 (5)

125 = x³ - 1/x³ - 15

125 + 15 = x³ - 1/x³

∴ x³ - 1/x³  = 140

Therefore, the value of x cube minus one by x cube is 140

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