Question

if x2-4x+1=0 then the value of x2+1/x2

Answer 1

Answer

• x² + ¹/x² = 14

$\orange{\bigstar}$  Given  $\green{\bigstar}$

→ x² - 4x + 1 = 0

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

→ x - ¹/ₓ

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

$\rm x^2-4x+1=0\\\\\to \rm x^2-4x=-1\\\\\to \rm x(x-4)=-1\\\\\to \rm x-4=-\dfrac{1}{x}\\\\\to \rm x+\dfrac{1}{x}=4$

On squaring on both sides ,

$\to \rm \left( x+\dfrac{1}{x}\right)^2=(4)^2\\\\\to \rm x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x}=16\\\\\to \rm x^2+\dfrac{1}{x^2}+2=16\\\\\to \rm x^2+\dfrac{1}{x^2}=16-2\\\\\to \bf x^2+\dfrac{1}{x^2}=14\ \; \pink{\bigstar}$