SOLUTION: how do you find the real number of x^4+5x^2=6

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Question 826730: how do you find the real number of x^4+5x^2=6
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
ONE WAY:
Rename x%5E2=y to get y%5E2%2B5y=6 <--> y%5E2%2B5y-6=0 , then solve.
That change of variable turns the problem into an easier one, where you may clearly see the solution.
Factoring, you transform y%5E2%2B5y-6=0
into %28y%2B6%29%28y-1%29=0 ,
which has the solutions y=-6 and y=1 .
From y=1 you get x%5E2=1 with real solutions
highlight%28x=1%29 and highlight%28x=-1%29 .
You cannot get real solutions from y=-6-->x%5E2=-6 .

ANOTHER WAY:
Just say that you are factoring, like this
x%5E4%2B5x%5E2=6
x%5E4%2B5x%5E2-6=0
%28x%5E2%2B6%29%28x%5E2-1%29=0
x%5E2%2B6%29%28x%2B1%29%28x-1%29=0
where x%5E2%2B6%3E=6%3E0 for all x ,
and the other factors' zeros,
highlight%28x=1%29 and highlight%28x=-1%29 ,
are the only real solutions.