How do you solve the equation and identify any extraneous solutions for #3(x+1)^(4/3)= 48#?

Question

Avery Alexander · Accepted Answer

I found #x=7# and #x=-9#

Try this:

Ho provato a usare questo risultato nell'equazione originale e funziona.

Eva Abramson · Answer

undefined To solve the equation 3(x+1)^(4/3) = 48 and identify any extraneous solutions, follow these steps:

1. Divide both sides of the equation by 3 to isolate the expression (x+1)^(4/3): (x+1)^(4/3) = 16.

2. Cube both sides of the equation to eliminate the fractional exponent: [(x+1)^(4/3)]^3 = 16^3.

3. Simplify the left side of the equation by applying the exponent rule: (x+1)^4 = 4096.

4. Take the fourth root of both sides of the equation to isolate the expression (x+1): √[(x+1)^4] = √4096.

5. Simplify the left side of the equation by applying the root rule: x+1 = ±16.

6. Subtract 1 from both sides of the equation to solve for x: x = -1 ± 16.

7. Simplify the solutions: x = -1 + 16 or x = -1 - 16.

8. Calculate the solutions: x = 15 or x = -17.

9. To identify any extraneous solutions, substitute each solution back into the original equation and check if it satisfies the equation.

Therefore, the solutions to the equation 3(x+1)^(4/3) = 48 are x = 15 and x = -17, and there are no extraneous solutions.