Question

设A=根号3—（根号2）.B=2-（根号3）,C=（根号5）-2.求ABC大小关系,追加100分急

Answer 1

A = 3^(1/2) - 2^(1/2) = 1/[3^(1/2) + 2^(1/2)]

B = 2 - 3^(1/2) = 1/[2 + 3^(1/2)]

C = 5^(1/2) - 2 = 1/[5^(1/2) + 2]

因

5^(1/2) > 3^(1/2),

所以,

C < B.

又

2 > 2^(1/2)

所以,

B < A.

综合,有

C < B < A.