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The sum of the solutions of the equation...

The sum of the solutions of the equation `|sqrt(x)-2|+sqrt(x)(sqrt(x)-4)+2=0,(xgt0)` is equal to 2k. The value of k is ________

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To solve the equation \( |\sqrt{x} - 2| + \sqrt{x}(\sqrt{x} - 4) + 2 = 0 \) for \( x > 0 \), we will consider two cases based on the value of \( \sqrt{x} \). ### Step 1: Case 1 - When \( \sqrt{x} \geq 2 \) In this case, the absolute value can be simplified as follows: \[ |\sqrt{x} - 2| = \sqrt{x} - 2 \] ...
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