Question

if x plus one upon x equals to 7 find the value of x cube plus one upon x cube

Answer 1

x cube + (1/x) cube = x cube +(1/x) cube +3{x(1/4)}{x+(1/x)}

Answer 2

Answer:

Value of $x^{3}+\frac{1}{x^{3}}= 322$

Step-by-step explanation:

Given

$x+\frac{1}{x}=7$ ---(1)

On cubeing both sides of the equation (1) , we get

$\left(x+\frac{1}{x}\right)^{3}=7^{3}$

$\implies x^{3}+\left(\frac{1}{x}\right)^{3}+3x\times \frac{1}{x}(x+\frac{1}{x})= 343$

$\implies x^{3}+\left(\frac{1}{x}\right)^{3}+3\times 7= 343$ /* From (1) */

$\implies x^{3}+\frac{1}{x^{3}}+21= 343$

$\implies x^{3}+\frac{1}{x^{3}}= 343 - 21$

$\implies x^{3}+\frac{1}{x^{3}}= 322$

Therefore,

Value of $x^{3}+\frac{1}{x^{3}}= 322$

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