If (x − 1/x) = 7, Find the value of

Question:

If $(x-1 / x)=7$, Find the value of $x^{3}-1 / x^{3}$

 

Solution:

Given, If $(x-1 / x)=7$

We know that, $(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b) \ldots 1$

Substitute $(x-1 / x)=7$ in eq 1

$(x-1 / x)^{3}=x^{3}-1 / x^{3}-3(x * 1 / x)(x-1 / x)$

$7^{3}=x^{3}-1 / x^{3}-3(x-1 / x)$

$343=x^{3}-1 / x^{3}-\left(3^{*} 7\right)$

$343=x^{3}-1 / x^{3}-21$

$343+21=x^{3}-1 / x^{3}$

$x^{3}-1 / x^{3}=364$

hence, the result is $x^{3}-1 / x^{3}=364$

 

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