+128578 x^2 + 3x + 3/x + 1/x^2 = 26 multiply through by x^2
x^4 + 3x^3 + 3x + 1 = 26x^2 rearrange
x^4 + 3x^3- 26x^2 + 3x + 1 = 0
This will factor as
(x^2 -4x + 1)(x^2 +7x + 1) = 0
And using the quadratic formula x = (4 ±√12)/2 = 2 ±√3
And x = (-7±√45)/2
But 2 +√3 is what we're looking for...so...a = 3, b = 2 and a + b = 5
+128578 x^2 + 3x + 3/x + 1/x^2 = 26 multiply through by x^2
x^4 + 3x^3 + 3x + 1 = 26x^2 rearrange
x^4 + 3x^3- 26x^2 + 3x + 1 = 0
This will factor as
(x^2 -4x + 1)(x^2 +7x + 1) = 0
And using the quadratic formula x = (4 ±√12)/2 = 2 ±√3
And x = (-7±√45)/2
But 2 +√3 is what we're looking for...so...a = 3, b = 2 and a + b = 5
