If x-1-x-5- find the value of x3-1-x3-

X 1/x=5 Cubing both sides (x 1/x )^3=(5)^3 ⇒ x^3 1/x^3 3(x 1/x )=125 ⇒ x^3 1/x^3 3× 5 = 125 ⇒ x^3 1/x^3 15=125 ⇒ x^3 1/x^3=125+15=140 ∴ x^3 1/x^3=140 ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If x-1/x=5, f...

Question

If $x - \frac{1}{x} = 5$ , find the value of $x^{3} - \frac{1}{x^{3}}$ .

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Solution

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

Cubing both sides

${(x - \frac{1}{x})}^{3} = (5)^{3} \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 (x - \frac{1}{x}) = 125 \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times 5 = 125 \Rightarrow x^{3} - \frac{1}{x^{3}} - 15 = 125 \Rightarrow x^{3} - \frac{1}{x^{3}} = 125 + 15 = 140 ∴ x^{3} - \frac{1}{x^{3}} = 140$

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If x−1x=5, find the value of x3−1x3.

x−1x=5 Cubing both sides (x−1x)3=(5)3⇒ x3−1x3−3(x−1x)=125⇒ x3−1x3−3×5=125⇒ x3−1x3−15=125⇒ x3−1x3=125+15=140∴ x3−1x3=140

If $x - \frac{1}{x} = 5$ , find the value of $x^{3} - \frac{1}{x^{3}}$ .