What is the answer to x^{4/3}-5x^{2/3}-36=0 ?

The answer to x^{4/3}-5x^{2/3}-36=0 is x=27,x=-27

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x^{4/3}-5x^{2/3}-36=0

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} - 36 = 0

x = 27, x = - 27

Solution steps

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} - 36 = 0

Use the following exponent property

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

x^{\frac{4}{3}} = (x^{\frac{1}{3}})^{4}, x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

(x^{\frac{1}{3}})^{4} - 5 (x^{\frac{1}{3}})^{2} - 36 = 0

Rewrite the equation with

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

u^{4} - 5 u^{2} - 36 = 0

Solve

u^{4} - 5 u^{2} - 36 = 0 : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

x^{\frac{1}{3}} = 3 : x = 27

Solve

x^{\frac{1}{3}} = - 3 : x = - 27

x = 27, x = - 27

Verify Solutions:

x = 27

True

, x = - 27

True

The solutions are

x = 27, x = - 27

5 + x + 14 = x + 34

3 x - 10 = 2

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

4 \frac{x}{( x + 1 )} + 3 \frac{( x + 1 )}{x} = 8

\frac{x}{8} = \frac{x}{18}

What is the answer to x^{4/3}-5x^{2/3}-36=0 ?
The answer to x^{4/3}-5x^{2/3}-36=0 is x=27,x=-27
Solve for x: x^{4/3}-5x^{2/3}-36=0
The solution is x=27,x=-27