题目

已知xy分别为8-(根号11)的整数部分和小数部分,求2xy-y^2的值

提问时间：2020-10-13

答案

8 - (11)^(1/2) = 4 + 4 - (11)^(1/2).
0 < 4 - (11)^(1/2) = [16 - 11]/[4 + (11)^(1/2)]
= 5/[4 + (11)^(1/2)]
< 5/[4 + 1]
= 1
所以,
x = 4.
y = 4 - (11)^(1/2)
2xy - y^2 = -x^2 + 2xy - y^2 + x^2 = x^2 -(x-y)^2
= 4^2 - [4 - 4 + (11)^(1/2)]^2
= 16 - 11
= 5