Question

x+1/× =4 find x^2+1/x^2​

Answer 1

Given,

$\sf{\dfrac{x+1}{x}=4}$

First we have to find the value of x.

From the equation:

$\sf{\implies 1+\dfrac{1}{x}=4}$

$\sf{\implies \dfrac{1}{x}=4-1}$

$\sf{\implies \dfrac{1}{x}=3}$

$\sf{\implies x=\dfrac{1}{3}}$

∴ The value of x is 3.

Now we have t find  $\sf{x^2+\dfrac{1}{x^2}}$.

Applying the value of x to the equation:

$\sf{\implies (\dfrac{1}{3})^2+\dfrac{1}{(\dfrac{1}{3})^2}}$

$\sf{\implies \dfrac{1}{9}+\dfrac{1}{\dfrac{1}{9}}}$

$\sf{\implies \dfrac{1}{9}+9}$

$\sf{\implies \dfrac{81+1}{9}}$

$\sf{\implies \dfrac{82}{9}}$

$\huge{\boxed{\bold{\sf{\therefore x^2+\dfrac{1}{x^2}=\dfrac{82}{9}}}}}$