Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \(x=-63\) and \(x=65\).
Solution
Solve the equation \( 2(x-1)^{2 / 3}=32 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(2\left(x-1\right)^{\frac{2}{3}}=32\)
- step1: Divide both sides:
\(\frac{2\left(x-1\right)^{\frac{2}{3}}}{2}=\frac{32}{2}\)
- step2: Divide the numbers:
\(\left(x-1\right)^{\frac{2}{3}}=16\)
- step3: Simplify the expression:
\(x-1=\pm 16^{\frac{3}{2}}\)
- step4: Simplify:
\(x-1=\pm 64\)
- step5: Separate into possible cases:
\(\begin{align}&x-1=64\\&x-1=-64\end{align}\)
- step6: Calculate:
\(\begin{align}&x=65\\&x=-63\end{align}\)
- step7: Rewrite:
\(x_{1}=-63,x_{2}=65\)
The solution set for the equation \(2(x-1)^{2/3}=32\) is \(x=-63\) and \(x=65\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To solve the equation, start by dividing both sides by 2: \[ (x-1)^{2/3} = 16 \] Next, raise both sides to the power of \( \frac{3}{2} \) to eliminate the exponent: \[ x - 1 = 16^{3/2} \] Calculating \( 16^{3/2} \), we find that \( 16^{1/2} = 4 \), and \( 4^3 = 64 \). So: \[ x - 1 = 64 \] Finally, add 1 to both sides: \[ x = 65 \] The solution set is \( \{65\} \).
