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Solve for x: x^12 = (x-1)^12
Published on September 14, 2024
Algebra
Solve the equation x^12 = (x-1)^12 for x. The solution is x = 1/2.
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