Solve each equation by factoring or by making an appropriate substitution

Question

2t^1/3 + 3t^1/6 -2 = 0

answer is (1/64)

Answer 1

Let x = t^1/6

Note that

t^1/3 = (t^1/6)² = x²

The substitution is

2x² + 3x - 2 = 0

Use the quadratic formula.

x = {-3 ± √[3² - 4(2)(-2)]} / [2(2)] = (-3 ± 5) / 4

x = 1/2 or -2

Test the two solutions.

t = x⁶

t = (1/2)⁶ = 1/2⁶ = 1/64

Plug this value of t into the original equation. It works.

t = (-2)⁶ = 64

If you plug this value of t into the original equation, it does not work. So the only solution is

t = 1/64