What are the real roots of the equation 8/x^4 + 5/x^2 = 3?
Solution: 8/x^4 + 5/x^2 = 3 …(1)
Let m = 1/x^2 so that (1) becomes
8m^2+5m–3 = 0
(8m-3)(m+1) = 0
So m = 3/8 or -1.
Discard m = -1 and we are left with m = 3/8 or x = 8/3
x = ±√(3/8). Answer.
Check: 8/x^4 + 5/x^2 = 3
LHS = 8*(√(8/3))^4 + 5*(√(8/3))^2
= 8*3*3/(8*8) + 5*3/8
= 9/8 + 15/8
= 24/8 = 3 = RHS. Correct