Question

If X^2+1/x^2=98, find X^3+1/X^3 ?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of $x^3+\dfrac{1}{x^3}$ is 970.

Step-by-step explanation:

It is given that,

$x^2+\dfrac{1}{x^2}=98$

Adding 2 both sides of the above equation

$x^2+\dfrac{1}{x^2}+2=98+2\\\\x^2+\dfrac{1}{x^2}+2=100\\\\(x+\dfrac{1}{x})^2=100\\\\x+\dfrac{1}{x}=10\ .....(1)$

Cubing equation (1) we get :

$(x+\dfrac{1}{x})^3=1000\\\\x^3+\dfrac{1}{x^3}+3x+\dfrac{3}{x}=1000\\\\x^3+\dfrac{1}{x^3}+3(x+\dfrac{1}{x})=1000$

Using equation (1) in above equation, we get :

$x^3+\dfrac{1}{x^3}+3(x+\dfrac{1}{x})=1000\\\\x^3+\dfrac{1}{x^3}=1000-3\times 10\\\\x^3+\dfrac{1}{x^3}=970$

So, the value of $x^3+\dfrac{1}{x^3}$ is 970.

Learn more,

Algebra

https://brainly.in/question/69991