What is the answer to cube root of x^2}-6=5\sqrt[3]{x ?

The answer to cube root of x^2}-6=5\sqrt[3]{x is x=-1,x=216

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cube root of x^2}-6=5\sqrt[3]{x

3 x^{2} - 6 = 5 3 x

x = - 1, x = 216

Solution steps

3 x^{2} - 6 = 5 3 x

Use the following exponent property

: a^{n} = (m a)^{(n \cdot m)}

x^{2} = (3 x)^{(2 \cdot 3)}

3 (3 x)^{6} - 6 = 5 3 x

Rewrite the equation with

3 x = u

3 u^{6} - 6 = 5 u

Solve

3 u^{6} - 6 = 5 u : u = - 1, u = 6

u = - 1, u = 6

Substitute back

u = 3 x,

solve for

x

Solve

3 x = - 1 : x = - 1

Solve

3 x = 6 : x = 216

x = - 1, x = 216

Verify Solutions:

x = - 1

True

, x = 216

True

The solutions are

x = - 1, x = 216

y + 6 = 12

6 x^{\frac{7}{2}} = 48 x^{2}

10 x + 10 = x + 1

x + 1 + x - 2 = 3

x = - x

What is the answer to cube root of x^2}-6=5\sqrt[3]{x ?
The answer to cube root of x^2}-6=5\sqrt[3]{x is x=-1,x=216
Solve for x: cube root of x^2}-6=5\sqrt[3]{x
The solution is x=-1,x=216