Expert: Sherman D. - 4/22/2008

Question
How do you solve this question? (I want the whole Enchilada! Its basic AS Level maths but I can't remember how to do it):

Find the real roots of the equation 18/x^4 + 1/x^2 = 4

Answer
18/(x^4) + 1/(x^2) = 4
multiply everything by x^4 to get rid of the fractions

18 + x^2 = 4x^4

4x^4 - x^2 - 18 = 0

now you can use the quadratic formula

x^2 = (-(-1) ± sqrt((-1)^2 - 4(4)(-18)))/(2(4))
x^2 = (1 ± sqrt(1 + 288))/8
x^2 = (1 ± sqrt(289))/8
x^2 = (1 ± 17)/8
x^2 = (-16/8) or (18/8)
x^2 = -2 or (9/4)

ANS : x
x = isqrt(2), -sqrt(2), (3/2), or (-3/2)

you can also use quickmath.com but it will only answer it for you so you can check your answers, but it won't show the work.