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Find the real roots of the equation
8/x^4 + 5/x^2 = 3
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Sagot :

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
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