Question

if x-1/x=3 find the value of x^3-1/x^3

Answer 1

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$x - \frac{1}{x} = 3 \\ {(x - \frac{1}{x} )}^{3} = {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) \\ 27 = {x}^{3 } - \frac{1}{ {x}^{3} } - 3 \times 3 \\ {x}^{3} - \frac{1}{ {x}^{3} } = 27 + 9 = 36$
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Answer 2

Answer:

36.

Step-by-step explanation:

• x - 1/x = 3
• So x² + 1/x² = 3² + 2 = 11.

x³ - 1/x³ = (x - 1/x ) ( x² + 1/x² + x·1/x)

              = 3 ( 11 + 1) = 3 x 12  = 36.