SOLUTION: Solve. (Enter your answers as a comma-separated list.) y^4-10y^2+9=0

Algebra ->  Equations -> SOLUTION: Solve. (Enter your answers as a comma-separated list.) y^4-10y^2+9=0      Log On


   

Question 1058311: Solve. (Enter your answers as a comma-separated list.)
y^4-10y^2+9=0
Answer by ikleyn(52778) About Me  (Show Source):
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Solve. (Enter your answers as a comma-separated list.)
y^4-10y^2+9=0
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t%5E4-10t%5E2%2B9 = 0.

Factor the left side

%28t%5E2-1%29%2A%28t%5E2-9%29 = 0.

This equation deploys in two independent equations:


1.  t%5E2-1 = 0  --->  t%5E2 = 1  --->  t = +/-1,

and

2.  t%5E2-9 = 0  --->  t%5E2 = 9  --->  t = +/-3.


Answer.  The solutions of the original equation are 1, -1, 3, and -3.