已知二次函数f(x)满足f(2x)+f(3X+1)=13x^2+6x-1 求f(x)

设f(x) = ax^2 + bx + c (a ≠ 0)
f(2x) = 4ax^2 + 2bx + c
f(3x+1) = a(3x+1)^2 + b(3x+1) + c = 9ax^2 + (6a+3b)x + a + b + 2c
f(2x) + f(3x+1) = 13ax^2 + (6a+5b)x + a + b + c = 13x^2 + 6x -1
比较系数：
a = 1
6a+5b = 6 +5b =6,　b= 0
a + b + 2c=1+0+ 2c= 1+ 2c = -1
c = -1
f(x) = x^2 -1