Question

If x+1/2 = 2 then value of x³+1/x³

Answer 1

Answer:

Answer is 793/216

I hope , it will help to understand

Answer 2

Answer:

$2$

Step-by-step explanation:

Its is given that $x+\frac{1}{x} = 2$

Cubing both sides

⇒ $(x+\frac{1}{x})^{3}= (2)^{3}$

We know that $(a+b)^{3} = a^{3} + b^{3} + 3ab(a+b)$

⇒ $(x)^{3} + (\frac{1}{x})^{3} + 3(x)(\frac{1}{x})(x+1/x) = 8$

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

We know that $x+\frac{1}{x} = 2$

⇒ $x^{3} + \frac{1}{x^{3}} +3(2) = 8$

⇒ $x^{3}+\frac{1}{x^{3}} = 8-6 = 2$

∴ $x^{3}+\frac{1}{x^{3}} = 2$