Solve x⁴ = 1
Polynomial equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = −1, x = 1 |
Step-by-step solution
4 steps-
1 Givenx^{4} = 1
Solve for x.
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2 Take the 4th root of both sides — remember both signs
A number and its negative give the same result when raised to an even power: 3² = 9 and (−3)² = 9. So if something squared equals k, that something is √k or −√k. Forgetting the minus sign loses a solution.
x = \pm 1 -
3 Solutionsx = 1\quad \text{or} \quad x = -1
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4 Check\begin{aligned}x = -1:\quad 1 = 1\quad\checkmark\\ x = 1:\quad 1 = 1\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −1 | 1 | 1 | ✓ |
| 1 | 1 | 1 | ✓ |
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