\( u = 0 \Rightarrow v = 0 \)
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- Solution: Let \( u = \sqrt{v} \), so \( v = u^2 \), and \( u \geq 0 \). Substitute:
- u^2 \cdot u - 5u^2 + 6u = 0 \Rightarrow u^3 - 5u^2 + 6u = 0
- So \( u = 0 \), \( u = 2 \), or \( u = 3 \). Since \( v = u^2 \), the corresponding roots are:
- \( u = 2 \Rightarrow v = 4 \)
- \( u = 3 \Rightarrow v = 9 \)
- All roots are non-negative, so valid. The sum of the roots is \( 0 + 4 + 9 = 13 \).
