Question

If x + 1/x =√3 , then find the value of x^3 + 1/x^3

Answer 1

Answer:

0

Step-by-step explanation:

Given :

To find the value of : $x^3 + \frac{1}{x^3}$

if $x +\frac{1}{x}=\sqrt{3}$.

Solution :

We know that,

$(a + b)^3= a^3 + b^3 + 3ab(a + b)$

⇒ $(a + b)^3 - 3ab(a + b) = a^3 + b^3$

Here, by substituting, $a = x$ and $b = \frac{1}{x}$,

We get,

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

⇒ $(\sqrt{3})^3 - 3(\frac{1 \times x}{x} )(\sqrt{3}) = x^3 + \frac{1}{x^3}$

⇒ ⇒ $(\sqrt{3})^3 = \sqrt{3 \times 3 \times 3} = 3\sqrt{3}$ ,

⇒ ⇒ $- 3(\frac{1 \times x}{x} )(\sqrt{3}) = -3\sqrt{3}$

So,

⇒ $(\sqrt{3})^3 - 3(\frac{1 \times x}{x} )(\sqrt{3}) = 3\sqrt{3} - 3\sqrt{3} = 0$

∴ $x^3 + \frac{1}{x^3} = 0$