SOLUTION: solve 25x^4-20x^2+3=0

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Question 255297: solve
25x^4-20x^2+3=0
Found 3 solutions by richwmiller, checkley77, CharlesG2:
Answer by richwmiller(17219) About Me  (Show Source):
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
25x%5E4-20x%5E2%2B3=0
(5x^2-1)(5x^2-3)=0 ans.

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
solve
25x^4-20x^2+3=0
substitute y for x^2
25y^2-20y+3=0
now we got a equation of form a*y^2 + b*y + c = 0
a=25, b=-20, c=3
using quadratic formula
y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A25%2A3+%29%29%2F%282%2A25%29+
y+=+%2820+%2B-+sqrt%28+400-300+%29%29%2F50+
y+=+%2820+%2B-+sqrt%28+100+%29%29%2F50+
y+=+%2820+%2B-+10%29%2F50+
y1+=+%2820+%2B+10%29%2F50+=+30%2F50+=+3%2F5
y2+=+%2820+-+10%29%2F50+=+10%2F50+=+1%2F5
y1=3/5, y2=1/5
now going back to x
y=x^2
x=+- sqrt(y)
x1=+- sqrt(3/5)
x2=+- sqrt(1/5)