設(shè)a>0,b>0,a,x1,x2,b成等差數(shù)列a,y1,y2,b成等比數(shù)列,
∴x1 +x2 =a+b,y1 ?y2 =ab,且|a-b|≥|y1 -y2 |>0.
兩邊平方可得 a2-2ab+b2≥y12-2y1y2+y22>0.
又4ab=4y1 ?y2>0,
兩邊分別相加,可得 (a+b)2≥(y1+y2)2>0,
a+b≥y1+y2 >0,當(dāng)且僅當(dāng)a=b時(shí)等號(hào)成立.
故選B.
設(shè)a>0,b>0,a,x1,x2,b成等差數(shù)列a,y1,y2,b成等比數(shù)列,則x1+x2與y1+y2的大小關(guān)系是( ?。?A.x1+x2≤y1+y2 B.x1+x2≥y1+y2 C.x1+x2<y1+y2 D.x1+x2>y1+y2
設(shè)a>0,b>0,a,x1,x2,b成等差數(shù)列a,y1,y2,b成等比數(shù)列,則x1+x2與y1+y2的大小關(guān)系是( ?。?br/>A. x1+x2≤y1+y2
B. x1+x2≥y1+y2
C. x1+x2<y1+y2
D. x1+x2>y1+y2
B. x1+x2≥y1+y2
C. x1+x2<y1+y2
D. x1+x2>y1+y2
數(shù)學(xué)人氣:598 ℃時(shí)間:2020-03-22 02:08:44
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