SOLUTION: Solve: 10x^4-17x^2+3=0 I originally came up with +/-(sqrt6)/2 and +/-(sqrt5)/5 After working through the problem the second time I came up with +/-(sqrt3/2)and +/-(sqrt1/5).

Question 303995: Solve:
10x^4-17x^2+3=0
I originally came up with +/-(sqrt6)/2 and +/-(sqrt5)/5
After working through the problem the second time I came up with +/-(sqrt3/2)and +/-(sqrt1/5).
Can someone please show me what I did wrong to come up with 2 different solutions? I think I missed something along the way of working through this problem.
Found 3 solutions by scott8148, mananth, richwmiller:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
factoring ___ (5x^2 - 1)(2x^2 - 3) = 0

not sure how you got the first solutions, but the second ones are correct
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
10x^4-17x^2+3=0
.
10x^4-15x^2-2x^2+3-0
.
5x^2(2x^2-3)-1(2x^2-3)=0
(5x^2-1)(2x^2-3)= 0
either 5x^2 =1
OR
2x^2=3
if 5x^2=1
x^2=1/5
x=+/- 1/sqrt5
if 2x^2=3
x^2=3/2
x= + /- sqrt(3/2)
Why the confusion you were right. There are 2 possibilities to satisfy the equation.
Ananth
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
There should 4 solutions
10x^4-17x^2+3=0
substitute z for x^2
10z^2-17z+3=0
factor
we want factors of 30 that add up to -17
-15 and -2
10z^2-15z-2z+3=0
5z*(2z-3)-1*(2z-3)=0
(5z-1)*(2z-3)=0
FOIL
10z^2-2z-15z+3=0
ok
plug x^2 back in for z
(5z-1)*(2z-3)=0
(5x^2-1)*(2x^2-3)=0
5x^2-1=0
5x^2=1
x^2=1/5
x=+-sqrt(1/5)
and
2x^2-3=0
2x^2=3
x^2=3/2
x=+-sqrt(3/2)
x=+-sqrt(1/5)

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