What is the answer to x^{3/2}+4x^{-1}-5x^0=4 ?

The answer to x^{3/2}+4x^{-1}-5x^0=4 is x=4,x\approx 0.46042…

Solve for x: x^{3/2}+4x^{-1}-5x^0=4

The solution is x=4,x\approx 0.46042…

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x^{\frac{3}{2}} + 4 x^{- 1} - 5 x^{0} = 4

x = 4, x \approx 0.46042 \dots

Solution steps

x^{\frac{3}{2}} + 4 x^{- 1} - 5 x^{0} = 4

Expand

x^{\frac{3}{2}} + 4 x^{- 1} - 5 x^{0} : x^{\frac{3}{2}} + \frac{4}{x} - 5

x^{\frac{3}{2}} + \frac{4}{x} - 5 = 4

Remove roots

x^{3} = \frac{16}{x ^{2}} - \frac{72}{x} + 81

Solve

x^{3} = \frac{16}{x ^{2}} - \frac{72}{x} + 81 : x = 4, x \approx 0.43090 \dots, x \approx 0.46042 \dots

x = 4, x \approx 0.43090 \dots, x \approx 0.46042 \dots

Verify Solutions:

x = 4

True

, x \approx 0.43090 \dots

False

, x \approx 0.46042 \dots

True

The solutions are

x = 4, x \approx 0.46042 \dots

9 x^{2} - 6 x + 1 = 5

6 4 x^{2} = 8

\frac{3 x}{( x - 2 x + 9 )} = 0

x^{2} + 8 x + 16 = x + 4

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

What is the answer to x^{3/2}+4x^{-1}-5x^0=4 ?
The answer to x^{3/2}+4x^{-1}-5x^0=4 is x=4,x\approx 0.46042…
Solve for x: x^{3/2}+4x^{-1}-5x^0=4
The solution is x=4,x\approx 0.46042…