Question

x+1/x=5 then find the value of x^3 +1/x^3​

Answer 1

Answer:

⇒ $x^3 + \frac{1}{x^3} = 110$

Step-by-step explanation:

Given :

$x+\frac{1}{x}= 5$

Then, find : $x^3 + \frac{1}{x^3}$

Solution :

We know that,

⇒ $(a+b)^3=a^3+b^3+3ab(a+b)$

____

$x+\frac{1}{x}= 5$

By cubing both the sides,

We get,

⇒ $(x+\frac{1}{x})^3= (5)^3$

⇒ $x^3+\frac{1}{x^3} + 3(x)(\frac{1}{x})(x+\frac{1}{x}) = 5^3$

⇒ $x^3 + \frac{1}{x^3} + 3(x+\frac{1}{x}) = 125$

As,

$x+\frac{1}{x}= 5$

Then,

⇒ $x^3 + \frac{1}{x^3} + 3(5) = 125$

⇒ $x^3 + \frac{1}{x^3} + 15 = 125$

⇒ $x^3 + \frac{1}{x^3} = 125 - 15$

⇒ $x^3 + \frac{1}{x^3} = 110$

Answer 2

Step-by-step explanation:

approx 64 hope it helps you......