The sum of the solutions of the equation , (x

Engineering

Mathematics

Modulus Function and Related Inequalities

Question

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

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$| \sqrt{x} - 2 | + \sqrt{x} (\sqrt{x} - 4) + 2 = 0$

$| \sqrt{x} - 2 | + {(\sqrt{x})}^{2} - 4 \sqrt{x} + 2 = 0$

${| \sqrt{x} - 2 |}^{2} + | \sqrt{x} - 2 | - 2 = 0$

$| \sqrt{x} - 2 | = - 2 (not possible) or | \sqrt{x} - 2 | = 1$

$\sqrt{x} - 2 = 1, - 1$

$\sqrt{x} - 3, 1$

X = 9, 1

Sum = 10