Question

1
3. The value of x³-1/x³
when x-1/x
= 5
х​

Answer 1

Answer:

140

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\underline{ \underline{ \green { \sf \: Given:-}}}\:$

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

$\underline{ \underline{ \green{ \sf \: To \: Find:-}}}$

$\tt{x}^{3} - \frac{1}{ {x}^{3} }$

$\underline{ \underline{ \green{ \sf \: Solution:-}}}$

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

Cube on both sides

$\tt(x + \frac{1}{x} )^{3} = ( {5})^{3} \\ \leadsto \: \tt {x}^{3} - \frac{1}{ {x}^{3} } - 3(x - \frac{1}{x}) = 125\\ \tt \leadsto \: {x}^{3} - \frac{1}{ {x}^{3} } - 3(5) = 125 \\ \tt \leadsto \: {x}^{3} - \frac{1}{ {x}^{3} } - 15 = 125 \\ \tt \leadsto \: \underline{ \underline{ \underline{ \pink{ \boxed{ \blue{ \tt{x}^{3} - \frac{1}{ {x}^{3} } = 125+15= 140}}}}}}$