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Section 2.9 : Equations Reducible to Quadratic in Form

Solve each of the following equations.

1. \(8{x^6} + 215{x^3} - 27 = 0\)
2. \({x^{\frac{4}{3}}} - 13{x^{\frac{2}{3}}} + 36 = 0\)
3. \(32{x^{ - 10}} - 31{x^{ - 5}} - 1 = 0\)
4. \(x - 8\sqrt x + 15 = 0\)
5. \({x^{ - \frac{1}{2}}} - 13{x^{ - \frac{1}{4}}} + 30 = 0\)
6. \({x^{ - 6}} - 3{x^{ - 3}} - 28 = 0\)
7. \({x^{10}} - 1024 = 0\)
8. \({x^4} - 8{x^2} + 5 = 0\)
9. \(\displaystyle \frac{1}{{{x^4}}} + \frac{{10}}{{{x^2}}} + 22 = 0\)