✔ 最佳答案
(1) 1/x + 1/y = 2 , 1/x² + 1/y² = 1.5 , 求 1/x³ + 1/y³ 的值。
解:
1/x + 1/y = 2 ---------(1)
1/x² + 1/y² = 1.5 -----(2)
(1)² - (2),得:
1/x² + 1/y² + 2/(xy) - (1/x² + 1/y²) = 4 - 1.5
2/(xy) = 2.5 ----------(3)
(1) × (2),得:
1/x³ + 1/y³ + 1/(x²y) + 1/(xy²) = 3
1/x³ + 1/y³ + (1/x + 1/y) / (xy) = 3 【把(1)代入】
1/x³ + 1/y³ + 2/(xy) = 3 【把(3)代入】
1/x³ + 1/y³ + 2.5 = 3
1/x³ + 1/y³ = 0.5
(2) x + y = 2 , x² + y² = 1.5 , 求 x³ + y³ 的值。
解:
x + y = 2 ---------(1)
x² + y² = 1.5 -----(2)
(1)² - (2),得:
x² + y² + 2xy - (x² + y²) = 4 - 1.5
2xy = 2.5 ----------(3)
(1) × (2),得:
x³ + y³ + x²y + xy² = 3
x³ + y³ + xy (x + y) = 3 【把(1)代入】
x³ + y³ + 2xy = 3 【把(3)代入】
x³ + y³ + 2.5 = 3
x³ + y³ = 0.5