Question

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

Answer 1

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