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

The answer to (x-2)^{2/3}+(x-2)^{1/3}-2=0 is x=3,x=-6

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(x-2)^{2/3}+(x-2)^{1/3}-2=0

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

x = 3, x = - 6

Solution steps

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

Use the following exponent property

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

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

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

Rewrite the equation with

(x - 2)^{\frac{1}{3}} = u

u^{2} + u - 2 = 0

Solve

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

u = 1, u = - 2

Substitute back

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

solve for

x

Solve

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

Solve

(x - 2)^{\frac{1}{3}} = - 2 : x = - 6

x = 3, x = - 6

Verify Solutions:

x = 3

True

, x = - 6

True

The solutions are

x = 3, x = - 6

3 x - 27 = 0

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

- 3 x - 2 + 7 = 3

\frac{( x ^{0.7} + 7 x ) 5 + 3}{4} = 5

c^{2} - 4 + 2 = c

What is the answer to (x-2)^{2/3}+(x-2)^{1/3}-2=0 ?
The answer to (x-2)^{2/3}+(x-2)^{1/3}-2=0 is x=3,x=-6
Solve for x: (x-2)^{2/3}+(x-2)^{1/3}-2=0
The solution is x=3,x=-6