SOLUTION: solve x^4-5x^2+6=0

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Question 18866: solve x^4-5x^2+6=0
Answer by xcentaur(357)   (Show Source): You can put this solution on YOUR website!
x^4-5x^2+6=0
Substitute y=x^2
y^2-5y+6=0
(y-3)(y-2)=0
y=3,2


y=x^2
therefore,
x^2=3,x^2=2
x=sqrt(3),x=sqrt(2)


This gives us all the four values of x
How?
For example sqrt(16)=-4,+4
This is because when a number is squared,
-*-=+ and +*+=+
In other words,a negative number squared is positive,a positive number squared is also positive,so -4 or +4 squared will give the same result.


So our correct answer is:
x=+sqrt(3),-sqrt(3),+sqrt(2),-sqrt(2)


Hope this helps,
Prabhat

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