Math, asked by sujatashailesh34, 6 months ago

x + 1/x = 5/2
find 'x^3 + 1/x^3'

Answers

Answered by Anonymous

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x + 1/x = 5/2
find 'x^3 + 1/x^3'

Answered by Mefuck

Answer:

red {x^{3} - \frac{1}{x^{3}} } \green { = 24\sqrt{21} }

Step-by-step explanation:

Given \: x + \frac{1}{x} = 5 \: ---(1)

\left( x - \frac{1}{x} \right)^{2} = \left( x + \frac{1}{x} \right)^{2} - 4

= 5^{2} - 4 \: [ From \: (1) ]

= 25 - 4 \\= 21

\left( x - \frac{1}{x} \right) = \sqrt{ 21} \: ---(2)

x^{3} - \frac{1}{x^{3}} = \left( x - \frac{1}{x}\right)^{3} + 3\left( x - \frac{1}{x}\right)

\boxed { \pink { a^{3} - b^{3} = (a - b)^{3} + 3ab(a-b) }}

= ( \sqrt{21} )^{3} + 3\sqrt{21} \: [From \: (2) ]

= 21\sqrt{21} + 3\sqrt{21} \\= 24\sqrt{21}

Therefore.,

red {x^{3} - \frac{1}{x^{3}} } \green { = 24\sqrt{21} }

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