X+9/x=6,then x2+9/x2=?

Question

$x + \frac{9}{x} = 6, then x^{2} + \frac{9}{x^{2}} = ?$ $x+9/x=6,"then "x^2+9/x^2=?$

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Answer 1 · 2018-05-20T09:05:08

$10$ $10$ .

Given that, $x + \frac{9}{x} = 6$ $x+9/x=6$ .

$\Rightarrow \frac{x^{2} + 9}{x} = 6, or, x^{2} - 6 x + 9 = 0$ $rArr (x^2+9)/x=6, or, x^2-6x+9=0$ .

$\Rightarrow {(x - 3)}^{2} = 0$ $rArr (x-3)^2=0$ .

$\Rightarrow x = 3$ $rArr x=3$ .

$\Rightarrow x^{2} + \frac{9}{x^{2}} = 3^{2} + \frac{9}{3^{2}} = 9 + 1 = 10$ $rArr x^2+9/x^2=3^2+9/3^2=9+1=10$ .