Question

If x2 + 1/x2 = 66, find the value of x3 -1/x3

Answer 1

Answer: Our required value is 536.

Step-by-step explanation:

Since we have given that

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

We need to find the value of $x^3-\dfrac{1}{x^3}$

As we know that

if $x-\dfrac{1}{x}=A$,

then,

$x^2-\dfrac{1}{x^2}=A^2+2\\\\and\\\\x^3-\dfrac{1}{x^3}=A^3+3A$

First we consider,

$66=A^2+2\\\\66-2=A^2\\\\64=A^2\\\\A=8$

So, it becomes,

$x^3+\dfrac{1}{x^3}=A^3-3A=8^3+3\times 8=512+24=536$

Hence, our required value is 536.

Answer 2

Answer:

488

Step-by-step explanation:

The previous answer has a mistake in the last step

here's the correct one