SOLUTION: Solve. (Enter your answers as a comma-separated list.) t^4-13t^2+42=0

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Question 1058312: Solve. (Enter your answers as a comma-separated list.)
t^4-13t^2+42=0
Answer by ikleyn(52778) About Me  (Show Source):
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Solve. (Enter your answers as a comma-separated list.)
t^4-13t^2+42=0
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t%5E4-13t%5E2%2B42 = 0.

Factor the left side

%28t%5E2-6%29%2A%28t%5E2-7%29 = 0.

This equation deploys in two independent equations:


1.  t%5E2-6 = 0  --->  t%5E2 = 6  --->  t = +/-sqrt%286%29

and

2.  t%5E2-7 = 0  --->  t%5E2 = 7  --->  t = +/-sqrt%287%29.


Answer.  The solutions of the original equation are sqrt%286%29, -sqrt%286%29, sqrt%287%29, and -sqrt%287%29.