The sum of the solutions of the equation |sqr | vedclass

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(C) Let $t = \sqrt{x}$,where $t > 0$.The equation becomes $|t - 2| + t(t - 4) + 2 = 0$.$|t - 2| + t^2 - 4t + 2 = 0$.We can rewrite $t^2 - 4t + 2$ as $

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Let $t = \sqrt{x}$,where $t > 0$.The equation becomes $|t - 2| + t(t - 4) + 2 = 0$.$|t - 2| + t^2 - 4t + 2 = 0$.We can rewrite $t^2 - 4t + 2$ as $(t^2 - 4t + 4) - 2 = (t - 2)^2 - 2$.So,$|t - 2| + (t - 2)^2 - 2 = 0$.Let $u = |t - 2|$,then $u^2 + u - 2 = 0$.$(u + 2)(u - 1) = 0$.Since $u = |t - 2| \ge 0$,we must have $u = 1$.$|t - 2| = 1 \implies t - 2 = 1$ or $t - 2 = -1$.$t = 3$ or $t = 1$.Since $t = \sqrt{x}$,we have $\sqrt{x} = 3 \implies x = 9$ and $\sqrt{x} = 1 \implies x = 1$.The sum of the solutions is $9 + 1 = 10$.

The sum of the solutions of the equation $|\sqrt{x} - 2| + \sqrt{x}(\sqrt{x} - 4) + 2 = 0$ for $x > 0$ is equal to

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