Question

If X+1/x =3 find x^2 + 1/x^2

Answer 1

Answer:

Step-by-step explanation:

x+1/x=3

squaring both sides

(x+1/x)^2=3^2

9=x^2+1/x^2+2(x*1/x)

9=x^2+1/x^2+2

9-2=x^2+y^2

x^2+y^2=7

Answer 2

Step-by-step explanation:

Given

${x}{+}\frac{1}{x}{=}{3}$ ===> 1

Squaring on both sides

( x - 1 / x )² = 3²

x² + 1 / x² - 2 * x * ( 1 / x ) = 9

Use formula

( a - b )² = a² + b² - 2ab

x² + 1 / x² - 2 = 9

x² + 1 / x² = 9 + 2

x² + 1 / x² = 11

$\therefore\frac{x^2~+~1}{x^2} {=} {11}$