Let x be a positive number such that 2x2=4x+9. If x can be written in simplified form as a+√bc such that a, b, and c are positive integers, what is a+b+c?
Rearrange as
2x^2 - 4x - 9 = 0
x = 4 + sqrt [ 4^2 - 4 * 2 * - 9 ]
_________________________
2 * 2
4 + sqrt [ 88]
_____________
4
4 + 2sqrt (22)
____________
2 + sqrt (22)
2
a = 2 b = 22 c = 2
Sum = 26
