Question

25 points! Please help and solve step by step. Solve for x and check for extraneous solutions.

(X-2)^2/3 + 13 = 5

Answer 1

No real solutions

Imaginary/complex solutions:

x = 2 +/- 16sqrt(2)i

Explanation:

(X-2)^2/3 + 13 = 5

(X-2)^2/3 = -8

(X - 2)² = (-8)³

X - 2 = +/- sqrt(-512)

No real solution

x = 2 +/- 16sqrt(2)i

(2 +/- 16sqrt(2)i - 2)^⅔ + 13 = 5

[(+/- 16sqrt(2)i)²]^⅓ + 13 = 5

(-512)^⅓ + 13 = 5

-8 + 13 = 5

5 = 5

Answer 2

no solutions

Explanation:

(X-2)^2/3 + 13 = 5

Subtract 13 from each side

(X-2)^2/3 + 13-13 = 5-13

(x-2) ^2/3 = -8

Raise each to the 3/2 power

(x-2) ^2/3 ^3/2= -8^3/2

(x-2) = (-512) ^1/2

We cannot take the square root of a negative number and remain in the real number system

There are no solutions