Solve for x: x^12 = (x-1)^12

Published on September 14, 2024

Question

\( \begin{array}{c}x^{12}=(x-1)^{12} \\ x=?\end{array} \)

Answer

Here’s how to solve the equation :
1. Take the 12th root of both sides:
To get rid of the exponents, we’ll take the 12th root of both sides of the equation. Remember that taking an even root introduces both positive and negative solutions:
This simplifies to:
2. Solve the two resulting equations:
Now we have two equations to solve:
  • Case 1:
    • x = x - 1
    • 0 = -1 (This equation has no solution)
  • Case 2:
    • x = -(x - 1)
    • x = -x + 1
    • 2x = 1
    • x = 1/2
Answer:
The only solution to the equation is .
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