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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 \( x > 0 \) and find the value of \( k \) such that the sum of the solutions is equal to \( 2k \), we can follow these steps: ### Step 1: Rewrite the equation We start with the equation: \[ |\sqrt{x} - 2| + \sqrt{x}(\sqrt{x} - 4) + 2 = 0 \] ...
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