Solve for x (x+3)^(2/3)=4

Problem

(x+3)(2/3)=4

Solution

1. Raise both sides to the power of 3/2 to isolate the term x+3

((x+3)(2/3))(3/2)=4(3/2)

2. Simplify the left side by multiplying the exponents, which results in an exponent of 1

x+3=4(3/2)

3. Evaluate the right side by taking the square root of 4 and then cubing the result. Note that since the denominator of the exponent is even, we consider the positive root first.

x+3=(√(,4))3

x+3=2

x+3=8

4. Isolate x by subtracting 3 from both sides of the equation.

x=8−3

x=5

5. Check for other solutions by considering the negative root, as the original equation involves squaring the term (x+3)(1/3)

x+3=−8

x=−11

6. Verify the solutions by substituting them back into the original equation.

(−11+3)(2/3)=(−8)(2/3)=((−8)(1/3))2=(−2)2=4

(5+3)(2/3)=(8)(2/3)=((8)(1/3))2=(2)2=4

Final Answer

(x+3)(2/3)=4⇒x=5,−11

Want more problems? Check here!