What is the answer to 6x^{-2/3}-13x^{-1/3}-5=0 ?

The answer to 6x^{-2/3}-13x^{-1/3}-5=0 is x=-27,x= 8/125

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6x^{-2/3}-13x^{-1/3}-5=0

6 x^{- \frac{2}{3}} - 13 x^{- \frac{1}{3}} - 5 = 0

x = - 27, x = \frac{8}{125}

Decimal Notation

x = - 27, x = 0.064

Solution steps

6 x^{- \frac{2}{3}} - 13 x^{- \frac{1}{3}} - 5 = 0

Expand

6 x^{- \frac{2}{3}} - 13 x^{- \frac{1}{3}} - 5 : \frac{6}{x ^{\frac{2}{3}}} - \frac{13}{x ^{\frac{1}{3}}} - 5

\frac{6}{x ^{\frac{2}{3}}} - \frac{13}{x ^{\frac{1}{3}}} - 5 = 0

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

\frac{6}{( x ^{\frac{1}{3}} ) ^{2}} - \frac{13}{x ^{\frac{1}{3}}} - 5 = 0

Rewrite the equation with

x^{\frac{1}{3}} = u

\frac{6}{u ^{2}} - \frac{13}{u} - 5 = 0

Solve

\frac{6}{u ^{2}} - \frac{13}{u} - 5 = 0 : u = - 3, u = \frac{2}{5}

u = - 3, u = \frac{2}{5}

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

x^{\frac{1}{3}} = - 3 : x = - 27

Solve

x^{\frac{1}{3}} = \frac{2}{5} : x = \frac{8}{125}

x = - 27, x = \frac{8}{125}

Verify Solutions:

x = - 27

True

, x = \frac{8}{125}

True

The solutions are

x = - 27, x = \frac{8}{125}

5 x + 41 + 7 = 2 x

a^{\frac{3}{4}} = 81

x - 3 = 3 x - 11

x + 51 - 18 = - 11

What is the answer to 6x^{-2/3}-13x^{-1/3}-5=0 ?
The answer to 6x^{-2/3}-13x^{-1/3}-5=0 is x=-27,x= 8/125
Solve for x: 6x^{-2/3}-13x^{-1/3}-5=0
The solution is x=-27,x= 8/125