Question

设a=√3-√2.b=2-√3.c=√5-2.则a.b.c的大小关系是?

解出的过程?能用其他方法做吗?这个没学呢

Answer 1

解：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.

Answer 2

a大于b大于c

Answer 3

1/a=√3+√2.
1/b=2+√3.
1/c=√5+2

1/a<1/b<1/c

则a>b>c