有條數唔識計?!

(a)

f (x+2)
= (x+2)^2 - k(x+2)
= (x^2 + 4x + 4) - kx - 2k
= x^2 + (4-k)x + (4-2k)

f (x-2)
= (x-2)^2 - k(x-2)
= (x^2 - 4x + 4) - kx + 2k
= x^2 - (4+k)x + (4+2k)


(b)

f(x+2)-f(x-2)=kx-32
[x^2 + (4-k)x + (4-2k)] - [x^2 - (4+k)x + (4+2k)] = kx - 32
x^2 + 4x - kx + 4 - 2k - (x^2 - 4x - kx + 4 + 2k) = kx - 32
x^2 + 4x - kx + 4 - 2k - x^2 + 4x + kx - 4 - 2k = kx - 32
8x - 4k = kx - 32
8x + 32 = kx + 4k
8x + 32 = (x+4)k
k = (8x+32)/(x+4)


(c)

f(x+2) = f(x-2) + 40
f(x+2) - f(x-2) = 40
kx - 32 = 40
kx = 72
[(8x+32)/(x+4)]x = 72
8x^2 + 32x = 72x + 288
8x^2 - 40x -288 = 0 (then solve the quadratic equation by quadratic formula)
x = 9 or -4

自己的功課自己做!!!