What is the answer to 3x(x-1)^{0.5}+2(x-1)^{1.5}=0 ?

The answer to 3x(x-1)^{0.5}+2(x-1)^{1.5}=0 is x=1

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3x(x-1)^{0.5}+2(x-1)^{1.5}=0

3 x (x - 1)^{0.5} + 2 (x - 1)^{1.5} = 0

x = 1

Solution steps

3 x (x - 1)^{0.5} + 2 (x - 1)^{1.5} = 0

Remove square roots

9 x^{3} - 9 x^{2} = 4 x^{3} - 12 x^{2} + 12 x - 4

Solve

9 x^{3} - 9 x^{2} = 4 x^{3} - 12 x^{2} + 12 x - 4 : x = 1, x = \frac{2}{5}, x = - 2

x = 1, x = \frac{2}{5}, x = - 2

Verify Solutions:

x = 1

True

, x = \frac{2}{5}

False

, x = - 2

False

The solution is

x = 1

6 x + 9 = x

- 3 8 - 2 v = - 6

0.42857 = (\frac{120}{x})^{3.5}

4 x = 5

What is the answer to 3x(x-1)^{0.5}+2(x-1)^{1.5}=0 ?
The answer to 3x(x-1)^{0.5}+2(x-1)^{1.5}=0 is x=1
Solve for x: 3x(x-1)^{0.5}+2(x-1)^{1.5}=0
The solution is x=1