Question

if [x+1/x]=4 find the value of [x²+1/x²]​

Answer 1

Answer :

$\boxed{\bf x^2+\frac{1}{x^2}=14}$

Step-by-step explanation :

$x^2+\frac{1}{x^2} =? \\\\ x+\frac{1}{x}=4 \\\\ squaring \ on \ both \ sides, \\\\ (x+\frac{1}{x})^2=4^2 \\\\ x^2+(\frac{1}{x})^2+2(x)(\frac{1}{x})=16 \\\\ x^2+\frac{1}{x^2}+2=16 \\\\ x^2+\frac{1}{x^2}=16-2\\\\ x^2+\frac{1}{x^2}=14$

$\boxed{\bf \underline{FORMULA}: (a+b)^2=a^2+b^2+2ab}$

Answer 2

Refer the attachment.......