Question

x2+1/x2=66 find value of x3-1/x3

Answer 1

This is the answer....

Answer 2

Answer:

The required value is $x^3-\frac{1}{x^3}=536$

Step-by-step explanation:

Given : $x^2+\frac{1}{x^2}=66$

To find : The value of  $x^3-\frac{1}{x^3}$

Solution :

$x^2+\frac{1}{x^2}=66$

Subtract and add $2\times x\times \frac{1}{x}$

$x^2+\frac{1}{x^2}-2\times x\times \frac{1}{x}+2\times x\times \frac{1}{x}=66$

$(x-\frac{1}{x})^2=66-2\times x\times \frac{1}{x}$

$(x-\frac{1}{x})^2=64$

Taking root both side,

$x-\frac{1}{x}=8$

Cubing both side,

$(x-\frac{1}{x})^3=8^3$

$x^3-\frac{1}{x^3}-3\times x\times \frac{1}{x}(x-\frac{1}{x})=512$

$x^3-\frac{1}{x^3}-3\times(8)=512$

$x^3-\frac{1}{x^3}=512+24$

$x^3-\frac{1}{x^3}=536$

So, The required value is $x^3-\frac{1}{x^3}=536$