If x + 81/x = 18 where x > 0, then the value of x^2 +162/(x^2) is :

If $x + \frac{81}{x} = 18$ where x > 0,

then the value of $x^2 +\frac{162}{x^2}$ = ?

$x + \frac{81}{x} = 18$

x² + 81 = 18x

= x² - 18x + 81 = 0

= x² - 9x - 9x + 81 = 0

= x(x - 9) - 9(x - 9) = 0

= (x - 9) (x - 9) = 0

= x = 9

Put the value of x in $x^2 +\frac{162}{x^2}$ = $9^2 +\frac{162}{9^2}$ = 83