If x-1-x-5- then x3-1-x3-5x2-1-x2-x-1-x is equal to

The correct option is D 0 (x^3 + 1/x^3 ) 5 ( x^2 + 1/x^2 ) + ( x+1/x ) = ( x+1/x )^3 3 ( x+1/x ) 5 [ ( x + 1/x )^2 2 ]+ ( x + 1/x ) = ( x + 1/x )^ ...

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Byju's Answer

Standard XII

Mathematics

Strictly Increasing Functions

If x+1/x=5, t...

Question

$I f x + \frac{1}{x} = 5, t h e n (x^{3} + \frac{1}{x^{3}}) - 5 (x^{2} + \frac{1}{x^{2}}) + (x + \frac{1}{x})$ is equal to

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Solution

The correct option is A
0

$(x^{3} + \frac{1}{x^{3}}) - 5 (x^{2} + \frac{1}{x^{2}}) + (x + \frac{1}{x}) = {(x + \frac{1}{x})}^{3} - 3 (x + \frac{1}{x}) - 5 [{(x + \frac{1}{x})}^{2} - 2] + (x + \frac{1}{x}) = {(x + \frac{1}{x})}^{3} - 5 {(x + \frac{1}{x})}^{2} - 2 (x + \frac{1}{x}) + 10 = 125 - 125 - 2 (5) + (10) = 0$

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Similar questions

Q. If

x = \frac{5 - \sqrt{21}}{2}

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Q. If

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

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l i m x \to 1 {∣ ∣ ∣ \begin{matrix} \frac{4}{x^{2} - x^{- 1}} - \frac{1 - 3 x + x^{2}}{1 - x^{3}} \end{matrix} ∣ ∣ ∣}^{- 1} + 3 ∣ ∣ ∣ \begin{matrix} \frac{x^{4} - 1}{x^{3} - x^{- 1}} \end{matrix} ∣ ∣ ∣

is equal to -

Q. If

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Ifx+1x=5,then(x3+1x3)−5(x2+1x2)+(x+1x) is equal to

The correct option is A 0 (x3+1x3)−5(x2+1x2)+(x+1x)=(x+1x)3−3(x+1x)−5[(x+1x)2−2]+(x+1x)=(x+1x)3−5(x+1x)2−2(x+1x)+10=125−125−2(5)+(10)=0

$I f x + \frac{1}{x} = 5, t h e n (x^{3} + \frac{1}{x^{3}}) - 5 (x^{2} + \frac{1}{x^{2}}) + (x + \frac{1}{x})$ is equal to