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1. 設 x² - 5x = 2, 求 x³ - 2x² - 17x - 1 之值為？

x² - 5x = 2 即 x³ - 5x² = 2x 即 x³ = 5x² + 2x

因此， x³ - 2x² - 17x - 1
= 5x² + 2x - 2x² - 17x - 1
= 3x² - 15x - 1
= 3(x² - 5x) - 1
= 3(2) - 1
= 6 - 1
= 5

2. 若一元二次方程式 x² - ax - 16 = 0 的兩根為相反數，4x² + 5x + b = 0 恰有一根為 0， 3x² - 10x + c = 0 的兩根互為倒數，則 a + b + c =？

x² - ax - 16 = 0 的兩根為相反數
即 兩根之和 = 0
即 a = 0

4x² + 5x + b = 0 恰有一根為 0
即 0 + 0 + b = 0
即 b = 0

3x² - 10x + c = 0 的兩根互為倒數
即 兩根之積 = 1
即 c/3 = 1
即 c = 3

因此， a + b + c = 0 + 0 + 3 = 3

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