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

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

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x+x^{3/2}-2x^{1/2}=0

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

x = 0, x = 1

Solution steps

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

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

Subtract

x^{2} - 4 x^{\frac{1}{2}} x + 4 x

from both sides

x^{3} - (x^{2} - 4 x^{\frac{1}{2}} x + 4 x) = x^{2} - 4 x^{\frac{1}{2}} x + 4 x - (x^{2} - 4 x^{\frac{1}{2}} x + 4 x)

Simplify

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

Factor

x^{3} - x^{2} + 4 x^{\frac{1}{2}} x - 4 x : x (x^{2} - x + 4 x^{\frac{1}{2}} - 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

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

x = 0, x = 1

Verify Solutions:

x = 0

True

, x = 1

True

The solutions are

x = 0, x = 1

8 - x + 1 = x - 1

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

3 x^{2} - 6 = 5 3 x

y + 6 = 12

6 x^{\frac{7}{2}} = 48 x^{2}

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