设a>0,b>0,a,x1,x2,b成等差数列a,y1,y2,b成等比数列,则x1+x2与y1+y2的大小关系是( ) A.x1+x2≤y1+y2 B.x1+x2≥y1+y2 C.x1+x2<y1+y2 D.x1+x2>y1+y2
问题描述:
设a>0,b>0,a,x1,x2,b成等差数列a,y1,y2,b成等比数列,则x1+x2与y1+y2的大小关系是( )
A. x1+x2≤y1+y2
B. x1+x2≥y1+y2
C. x1+x2<y1+y2
D. x1+x2>y1+y2
答
设a>0,b>0,a,x1,x2,b成等差数列a,y1,y2,b成等比数列,∴x1 +x2 =a+b,y1 •y2 =ab,且|a-b|≥|y1 -y2 |>0.两边平方可得 a2-2ab+b2≥y12-2y1y2+y22>0.又4ab=4y1 •y2>0,两边分别相加,可得 (a+...