教育/科学

求取值范围已知实数x,y满足x^3+y^3=128求x+y的取值

2007-10-04 19:11:58水***

已知实数x,y满足x^3+y^3=128求x+y的取值范围。求取值范围已知实数x,y满足x^3+y^3=128求x+y的取值范围。：(x+y)^2 ≥4xy x+y≥0时: 128 = x^3+y^3 = (x+y)?

(x+y)^2 ≥4xy x+y≥0时: 128 = x^3+y^3 = (x+y)^3 -3xy(x+y) ≥(x+y)^3 -3[(1/4)(x+y)^2](x+y) =(1/4)(x+y)^3 ==> 0 x+y ≥8，与x+y≤0矛盾因此，x+y的取值范围为：0< x+y ≤8

2007-10-04 20:41:14

很赞哦！ (247)