Question

设a=根号2，b=根号7-根号3，c=根号6-根号2，则abc的大小顺序是

Answer 1

a=√2=2/√2=4/(2√2)=4/(√2+√2),
b=√7-√3=(√7-√3)( √7+√3)/( √7+√3)=4/( √7+√3),
c=√6-√2=(√6-√2)( √6+√2)/( √6+√2)=4/( √6+√2)，
因为√2+√2<√6+√2<√7+√3
所以4/(√2+√2) >4/( √6+√2)>4/( √7+√3)
即a>c>b.

Answer 2

a=4/(2√2)
b=4/(√7+√3)
c=4/(√6+√2)
∵√7+√3>√6+√2
∴b<c
又∵(2√2)²=8
(√6+√2)²=8+4√3
∴2√2<√6+√2
∴a>c

∴b<c<a