Question

X+1/X=3 then what is the value of x²+1/x²​

Answer 1

Given :-

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

To Find :-

$\bigg(\sf x^2+\dfrac{1}{x^2}\bigg)$

Solution :-

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

Squaring both sides

$\sf\bigg(x+\dfrac{1}{x}\bigg)^2=(3)^2$

${\boxed{\sf (a+b)^2=a^2+2ab+b^2}}$

$\sf x^2+2\times x\times\dfrac{1}{x}+\dfrac{1}{x^2}=9$

$\sf x^2+\dfrac{1}{x^2}+2=9$

$\sf x^2+\dfrac{1}{x^2} =9-2$

$\sf x^2+\dfrac{1}{x^2} =7$

Hence

Value of x² + 1/x² is 7