What is the answer to x^4x^{1/3}=x ?

The answer to x^4x^{1/3}=x is x=0,x=1,x=-1

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x^4x^{1/3}=x

x^{4} x^{\frac{1}{3}} = x

x = 0, x = 1, x = - 1

Solution steps

x^{4} x^{\frac{1}{3}} = x

Move

x

to the left side

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

Factor

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

x (x^{\frac{1}{3}} x^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x^{\frac{1}{3}} x^{3} - 1 = 0 : x = 1, x = - 1

x = 0, x = 1, x = - 1

Verify Solutions:

x = 0

True

, x = 1

True

, x = - 1

True

The solutions are

x = 0, x = 1, x = - 1

(6 x - 4)^{\frac{1}{3}} + 4 = 0

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

x - 7 + 9 = 0

2 x^{2} - 5 x + 3 = 0

1.6 = \frac{( 171 ) ( w )}{60}