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

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

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

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

x = 0, x = 1

Solution steps

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

3 v = 2

x + 13 - 8 = - 2

4 x - 7 + 12 = 28

144 - x^{2} + x = 0

56 - r = r

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