If $x + \frac{81}{x} = 18$ where x > 0, then the value of $x^2 +\frac{162}{x^2}$ is :

78 83 85 81

83

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