What is the answer to x^{3/2}-8x^{-3/2}=7 ?

The answer to x^{3/2}-8x^{-3/2}=7 is x=4

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x^{3/2}-8x^{-3/2}=7

x^{\frac{3}{2}} - 8 x^{- \frac{3}{2}} = 7

x = 4

Solution steps

x^{\frac{3}{2}} - 8 x^{- \frac{3}{2}} = 7

Expand

x^{\frac{3}{2}} - 8 x^{- \frac{3}{2}} : x^{\frac{3}{2}} - \frac{8}{x ^{\frac{3}{2}}}

x^{\frac{3}{2}} - \frac{8}{x ^{\frac{3}{2}}} = 7

Factor

x^{\frac{3}{2}} - \frac{8}{x ^{\frac{3}{2}}} : \frac{( x - 2 ) ( x ^{2} + 2 x + 4 )}{x ^{\frac{3}{2}}}

\frac{( x - 2 ) ( x ^{2} + 2 x + 4 )}{x ^{\frac{3}{2}}} = 7

Square both sides:

x^{3} - 16 + \frac{64}{x ^{3}} = 49

x^{3} - 16 + \frac{64}{x ^{3}} = 49

Solve

x^{3} - 16 + \frac{64}{x ^{3}} = 49 : x = 4, x = 1

x = 4, x = 1

Verify Solutions:

x = 4

True

, x = 1

False

The solution is

x = 4

x^{\frac{1}{2}} - 4 x^{\frac{1}{4}} = 0

\frac{2 x ^{2} + 4}{x ^{2} + 4} = 0

x + 4 - x - 4 = 2

x + 16 = 0

2 - y = y^{2} - 12

What is the answer to x^{3/2}-8x^{-3/2}=7 ?
The answer to x^{3/2}-8x^{-3/2}=7 is x=4
Solve for x: x^{3/2}-8x^{-3/2}=7
The solution is x=4