Question

if x+1/x=4 find the value of x^3+1/x^3 pls help

Answer 1

Answer:

52

Step-by-step explanation:

Given :

$x+\frac{1}{x} = 4$

Then,

$x^3 + \frac{1}{x^3}$ = ?

Solution :

We know that,

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

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

We get,

⇒ $(x+\frac{1}{x})^3 = 4^3$

⇒ $(x)^3 + 3(x)(\frac{1}{x})(x + \frac{1}{x} ) + (\frac{1}{x} )^3 =64$

⇒ $x^3 + \frac{1}{x^3} + 3(1)(4) = 64$

⇒ $x^3 + \frac{1}{x^3} + 12 = 64$

⇒ $x^3 + \frac{1}{x^3} = 64 - 12$

⇒ $x^3 + \frac{1}{x^3} = 52$