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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