What is the answer to x^{-3}-9x^{-3/2}+8=0 ?

The answer to x^{-3}-9x^{-3/2}+8=0 is x=1,x= 1/4

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x^{-3}-9x^{-3/2}+8=0

x^{- 3} - 9 x^{- \frac{3}{2}} + 8 = 0

x = 1, x = \frac{1}{4}

Decimal

x = 1, x = 0.25

Solution steps

x^{- 3} - 9 x^{- \frac{3}{2}} + 8 = 0

Expand

x^{- 3} - 9 x^{- \frac{3}{2}} + 8 : \frac{1}{x ^{3}} - \frac{9}{x ^{\frac{3}{2}}} + 8

\frac{1}{x ^{3}} - \frac{9}{x ^{\frac{3}{2}}} + 8 = 0

Remove square roots

\frac{81}{x ^{3}} = \frac{1}{x ^{6}} + \frac{16}{x ^{3}} + 64

Solve

\frac{81}{x ^{3}} = \frac{1}{x ^{6}} + \frac{16}{x ^{3}} + 64 : x = 1, x = \frac{1}{4}

x = 1, x = \frac{1}{4}

Verify Solutions:

x = 1

True

, x = \frac{1}{4}

True

The solutions are

x = 1, x = \frac{1}{4}

3 x - 4 = 15

2 x = - 8

2 x - 3 = 10 - x

- 5 x + 1 + x + 4 = 3

3 x - 6 + 2 x + 6 + 1 = 0

What is the answer to x^{-3}-9x^{-3/2}+8=0 ?
The answer to x^{-3}-9x^{-3/2}+8=0 is x=1,x= 1/4
Solve for x: x^{-3}-9x^{-3/2}+8=0
The solution is x=1,x= 1/4