$x + x^{-1} = 98$

Algebra Level 2

If $x$ satisfies the equation $x + x^{-1} =98$ , what is the value of $\sqrt x + (\sqrt x)^{-1}$ ?

15 8 6 12 10 9

1 solution

Chew-Seong Cheong
Jan 11, 2017

$\begin{aligned} X & = \sqrt x + \frac 1{\sqrt x} \\ X^2 & = \left(\sqrt x + \frac 1{\sqrt x}\right)^2 \\ & = {\color{#3D99F6}x} + 2 + {\color{#3D99F6}\frac 1x} & \small \color{#3D99F6} \text{Given that } x + \frac 1x = 98 \\ & = {\color{#3D99F6}98} + 2 = 100 \\ \implies X & = \boxed{10} & \small \color{#3D99F6} \text{Note that } \sqrt x + \frac 1{\sqrt x} > 0 \end{aligned}$

x + x − 1 = 98 x + x^{-1} = 98 x + x − 1 = 9 8

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$x + x^{-1} = 98$