Variation

55.
(a)
y ∝ x(x + 1)²
Hence, y = kx(x + 1)² where k is a constant.

when x = 3, y = 36 :
(36) = k(3)(3 + 1)²
48k = 36
k = 3/4

Hence, y = 3x(x + 1)²/4


(b)
When x = 5 :
y = 3(5)(5 + 1)²/4
y = 135


(c)
x : y = 3 : 4
Let x = 3n and y = 4n

y = 3x(x + 1)²/4
4n = 3(3n)(3n + 1)²/4

Since n ≠ 0 :
4n/n = [3(3n)(3n + 1)²/4]/n
3(3)(3n + 1)²/4 = 4
9(3n + 1)² = 16
(3n + 1)² = 16/9
3n + 1 = 4/3 or 3n + 1 = -4/3
3n = 1/3 or 3n = -7/3
n = 1/9 or n = -7/9
4n = 4/9 or 4n = -28/9
y = 4/9 or y = -28/9