Question

If x²+1/x²=1 then find the value of x³+1/x³

Answer 1

Answer:

0

Step-by-step explanation:

$x^2 + \dfrac{1}{x^2} = 1\\\\{[x + \dfrac{1}{x}]}^2 = \sqrt{1} = 1\\\\\text{Hence}\:\: x + \dfrac{1}{x} = 1$

Now we know that,

$x^3 + \dfrac{1}{x^3} = ( x + \dfrac{1}{x} )\:( x^2 + \dfrac{1}{x^2} - x \times \dfrac{1}{x} )\\\\\implies x^3 + \dfrac{1}{x^3} = ( x + \dfrac{1}{x} )\:( x^2 + \dfrac{1}{x^2} - 1 )$

Substituting in the formula we get,

$\implies x^3 + \dfrac{1}{x^3} = ( 1 ) ( 1 - 1 )\\\\\implies x^3 + \dfrac{1}{x^3} = 1 ( 0 ) = 0$

Hence the value is 0.

Thanks !!

Answer 2

Answer:

0 .............................