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=8,x=-8

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

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

x = 8, x = - 8

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 = 2, u = - 2

u = 2, u = - 2

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 2 : x = 8

Solve

x^{\frac{1}{3}} = - 2 : x = - 8

x = 8, x = - 8

Verify Solutions:

x = 8

True

, x = - 8

True

The solutions are

x = 8, x = - 8

9 = x + 7

q - 21 = q + 7

\frac{- 2 x ^{2} + 8}{8 - x ^{2}} = 0

3 x + 10 = x + 2

6 + 4 x - 2 = 0

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=8,x=-8
Solve for x: x^{4/3}+5x^{2/3}-36=0
The solution is x=8,x=-8