Solve \(x^{\frac{2}{3}} - 5x^{\frac{1}{3}} + 6 = 0\).
Question 1 Report
Solve \(x^{\frac{2}{3}} - 5x^{\frac{1}{3}} + 6 = 0\).
Answer Details
Let \(u = x^{1/3}\), so \(x^{2/3} = u^2\). The equation becomes a quadratic:
\[u^2 - 5u + 6 = 0 \ \Rightarrow\ (u - 2)(u - 3) = 0\] \[u = 2 \quad\text{or}\quad u = 3\]Return to \(x\):
\[x^{1/3} = 2 \ \Rightarrow\ x = 2^3 = 8\] \[x^{1/3} = 3 \ \Rightarrow\ x = 3^3 = 27\]So \(x = 8\) or \(x = 27\).
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