求比（√3+√2）^6大的最小整数（）A.970B.971C.972D.969

Question

求比（√3+√2）^6大的最小整数（） A.970 B.971 C.972 D.969

Answer 1

解析,
(√3+√2)^6=(5+2√6)³
1000-(5+2√6)³
=10³-(5+2√6)³
=(5-2√6)*[100+(5+2√6)²+10(5+2√6)]
=100(5-2√6)+(5+2√6)+10
=100/(5+2√6)+(5+2√6)+10
设t=100/x+x【x>0】,那么t≥20,当且仅当x=10时取等号,
当x∈(0,10]时,t为减函数,
又5+2√69
因此,100/(5+2√6)+(5+2√6)+10>2*10+10=30,
100/(5+2√6)+(5+2√6)+101000-(5+2√6)³>30,那么,969+8/9