5Question: If a climate model predicts temperature changes over time with the equation $ u\sqrt{u} - 5u + 6\sqrt{u} = 0 $, find the sum of all real roots of the equation.
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- Solution: Let $ \sqrt{u} = x $, so $ u = x^2 $. Substituting into the equation gives:
- Factoring out $ x $:
- So the solutions for $ x $ are $ x = 0, 2, 3 $. Since $ x = \sqrt{u} $, we find the corresponding $ u $ values:
