Fractional Exponents?

How do I solve this? Step by step would be appreciated.

6x^(2 / 3) – 17x^(1 / 3) – 14 = 0

Top 1 Answers

A few days ago

MsMath

Favorite Answer

Use a substitution.

Let y = x^(1/3), then (y)^2 = (x^(1/3))^2 = x^(2/3)

Substituting you get

6y^2 – 17y – 14 = 0

Now factor.

(2y-7)(3y+2) = 0

2y – 7 = 0 or 3y+2 = 0

y = 7/2 or y = -2/3

Remember that y = x^(1/3); therefore,

x^(1/3) = 7/2 or x^(1/3) = -2/3

Raise each side to the third power

x = (7/2)^3 or x = (-2/3)^3

x = 343/8 or x = -8/27

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