What is the answer to x^{2/5}+3x^{1/5}-4=0 ?

The answer to x^{2/5}+3x^{1/5}-4=0 is x=1,x=-1024

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x^{2/5}+3x^{1/5}-4=0

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

x = 1, x = - 1024

Solution steps

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{2}{5}} = (x^{\frac{1}{5}})^{2}

(x^{\frac{1}{5}})^{2} + 3 x^{\frac{1}{5}} - 4 = 0

Rewrite the equation with

x^{\frac{1}{5}} = u

u^{2} + 3 u - 4 = 0

Solve

u^{2} + 3 u - 4 = 0 : u = 1, u = - 4

u = 1, u = - 4

Substitute back

u = x^{\frac{1}{5}},

solve for

x

Solve

x^{\frac{1}{5}} = 1 : x = 1

Solve

x^{\frac{1}{5}} = - 4 : x = - 1024

x = 1, x = - 1024

Verify Solutions:

x = 1

True

, x = - 1024

True

The solutions are

x = 1, x = - 1024

x + 5 = x - 7

8 = 14 - 5 x

3 - 3 x - 3 + x = 2

2 x + 7 - x - 3 = 1

What is the answer to x^{2/5}+3x^{1/5}-4=0 ?
The answer to x^{2/5}+3x^{1/5}-4=0 is x=1,x=-1024
Solve for x: x^{2/5}+3x^{1/5}-4=0
The solution is x=1,x=-1024