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

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

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

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

x = 0, x = 1

Solution steps

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{\frac{1}{2}} = 0 : x = 0

Solve

x - 1 = 0 : x = 1

x = 0, x = 1

Verify Solutions:

x = 0

True

, x = 1

True

The solutions are

x = 0, x = 1

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x^{\frac{2}{3}} - 7 x^{\frac{1}{3}} + 10 = 0

\frac{5}{6} x^{- \frac{1}{6}} = 1

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

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