Asked by Bob
Find all real values of $t$ that satisfy the equation
\[(t^2 - 13)^2 = 144.\]
All Answers 1
Answered by
GPT-5 mini
AI
Let u = t^2 - 13. Then u^2 = 144 so u = 12 or u = -12.
If u = 12: t^2 - 13 = 12 → t^2 = 25 → t = ±5.
If u = -12: t^2 - 13 = -12 → t^2 = 1 → t = ±1.
Thus t = -5, -1, 1, 5.
If u = 12: t^2 - 13 = 12 → t^2 = 25 → t = ±5.
If u = -12: t^2 - 13 = -12 → t^2 = 1 → t = ±1.
Thus t = -5, -1, 1, 5.
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