已知实数x,a,b,y成等差数列,x,c,d,y成等比数列,求(a+b)^2/cd的取值范围由题意可得:x+y=a+b且xy=cd所以:(a+b)的平方/(cd)=(x+y)²/(xy)=(x²+2xy+y²)/(xy)=x/y + y/x +2分两种情况:(1)x、y同号,则
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![已知实数x,a,b,y成等差数列,x,c,d,y成等比数列,求(a+b)^2/cd的取值范围由题意可得:x+y=a+b且xy=cd所以:(a+b)的平方/(cd)=(x+y)²/(xy)=(x²+2xy+y²)/(xy)=x/y + y/x +2分两种情况:(1)x、y同号,则](/uploads/image/z/6890129-17-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Ca%2Cb%2Cy%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2Cx%2Cc%2Cd%2Cy%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%B1%82%28a%2Bb%29%5E2%2Fcd%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E7%94%B1%E9%A2%98%E6%84%8F%E5%8F%AF%E5%BE%97%EF%BC%9Ax%2By%3Da%2Bb%E4%B8%94xy%3Dcd%E6%89%80%E4%BB%A5%EF%BC%9A%EF%BC%88a%2Bb%EF%BC%89%E7%9A%84%E5%B9%B3%E6%96%B9%2F%28cd%29%3D%28x%2By%29%26%23178%3B%2F%28xy%29%3D%28x%26%23178%3B%2B2xy%2By%26%23178%3B%29%2F%28xy%29%3Dx%2Fy+%2B+y%2Fx+%2B2%E5%88%86%E4%B8%A4%E7%A7%8D%E6%83%85%E5%86%B5%EF%BC%9A%EF%BC%881%EF%BC%89x%E3%80%81y%E5%90%8C%E5%8F%B7%2C%E5%88%99)
已知实数x,a,b,y成等差数列,x,c,d,y成等比数列,求(a+b)^2/cd的取值范围由题意可得:x+y=a+b且xy=cd所以:(a+b)的平方/(cd)=(x+y)²/(xy)=(x²+2xy+y²)/(xy)=x/y + y/x +2分两种情况:(1)x、y同号,则
已知实数x,a,b,y成等差数列,x,c,d,y成等比数列,求(a+b)^2/cd的取值范围
由题意可得:
x+y=a+b且xy=cd
所以:(a+b)的平方/(cd)
=(x+y)²/(xy)
=(x²+2xy+y²)/(xy)
=x/y + y/x +2
分两种情况:
(1)x、y同号,则由均值定理可得:
x/y + y/x ≥2根号[(x/y)*(y/x)]=2 (当且仅当x/y=y/x即x=y时取等号)
所以可得:x/y + y/x +2≥4 即(a+b)的平方/(cd)≥4
(2)x、y异号,-(x/y + y/x) ≥2,x/y + y/x≤-2,即(a+b)的平方/(cd)≤0
不懂,
已知实数x,a,b,y成等差数列,x,c,d,y成等比数列,求(a+b)^2/cd的取值范围由题意可得:x+y=a+b且xy=cd所以:(a+b)的平方/(cd)=(x+y)²/(xy)=(x²+2xy+y²)/(xy)=x/y + y/x +2分两种情况:(1)x、y同号,则
∵实数x,a,b,y成等差数列,∴x+y=a+b
∵x,c,d,y成等比数列∴xy=cd
代换化简(a+b)^2/cd=(x+y)²/(xy)
=(x²+2xy+y²)/(xy)
=x/y + y/x +2
∵对正数a、b有(a+b)/2≥√ab
∴(1)若x、y同号,可得:
x/y + y/x ≥2√[(x/y)*(y/x)]=2 (当且仅当x/y=y/x即x=y时取等号)
即(a+b)的平方/(cd)≥4
(2)若x、y异号,则-x/y,-y/x为正,(-x/y) +(- y/x) ≥2,∴ x/y + y/x≤-2,
即(a+b)的平方/(cd)≤0
这样解释能理解了吗?
楼主啊,您的追问是高中的基本不等式:如果A>0,B>0,则A+B≥2√AB,当且仅当A=B时取等号。。。其他的都是变式。。
答案已经非常清晰了,你哪里不懂?