A quantity Q equals the sum of three other quantities, the first of which is a constant, the second varies directly as x and the third varies directly as x². When x = 1; p = 52. when x = 2, p = 144 and when x = 3, p = 316. Find the constant.
Explanation:
Let p = A + Bx + Cx²
∴ A + B + C = 52 …(1)
A + 2B + 4C = 144 …(2)
A + 3B + 9C = 316 …(3)
(2) – (1) ⇒ B + 3C = 92 …(4)
(3) – (2) ⇒ B + 5C = 172 …(5)
(5) – (4) ⇒ 2C = 80
∴ C = 40 ⇒ B = -28
∴ A – 28 + 40 = 52
⇒ A = 40
Hence, 40.
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