几道数列与不等式的题.1.若a>0,b>0,且2a+b=1,求S=2√ab-4a^2-b^2的最大值.2.求S=1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/[n(n+1)(n+2)]的值.3.实数x、y满足y+x^2=0,0√代表根号,^2代表平方,*代表乘以,log(a)2代表以a
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![几道数列与不等式的题.1.若a>0,b>0,且2a+b=1,求S=2√ab-4a^2-b^2的最大值.2.求S=1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/[n(n+1)(n+2)]的值.3.实数x、y满足y+x^2=0,0√代表根号,^2代表平方,*代表乘以,log(a)2代表以a](/uploads/image/z/1160015-23-5.jpg?t=%E5%87%A0%E9%81%93%E6%95%B0%E5%88%97%E4%B8%8E%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%9A%84%E9%A2%98.1.%E8%8B%A5a%3E0%2Cb%3E0%2C%E4%B8%942a%2Bb%3D1%2C%E6%B1%82S%3D2%E2%88%9Aab-4a%5E2-b%5E2%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC.2.%E6%B1%82S%3D1%2F%281%2A2%2A3%29%2B1%2F%282%2A3%2A4%29%2B1%2F%283%2A4%2A5%29%2B%E2%80%A6%E2%80%A6%2B1%2F%5Bn%28n%2B1%29%28n%2B2%29%5D%E7%9A%84%E5%80%BC.3.%E5%AE%9E%E6%95%B0x%E3%80%81y%E6%BB%A1%E8%B6%B3y%2Bx%5E2%3D0%2C0%E2%88%9A%E4%BB%A3%E8%A1%A8%E6%A0%B9%E5%8F%B7%EF%BC%8C%5E2%E4%BB%A3%E8%A1%A8%E5%B9%B3%E6%96%B9%EF%BC%8C%2A%E4%BB%A3%E8%A1%A8%E4%B9%98%E4%BB%A5%EF%BC%8Clog%28a%292%E4%BB%A3%E8%A1%A8%E4%BB%A5a)
几道数列与不等式的题.1.若a>0,b>0,且2a+b=1,求S=2√ab-4a^2-b^2的最大值.2.求S=1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/[n(n+1)(n+2)]的值.3.实数x、y满足y+x^2=0,0√代表根号,^2代表平方,*代表乘以,log(a)2代表以a
几道数列与不等式的题.
1.若a>0,b>0,且2a+b=1,求S=2√ab-4a^2-b^2的最大值.
2.求S=1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/[n(n+1)(n+2)]的值.
3.实数x、y满足y+x^2=0,0
√代表根号,^2代表平方,*代表乘以,log(a)2代表以a为底,2的对数。log(a)(a^x+a^y)代表以a为底,a的x次方与a的y次方的和的对数。
几道数列与不等式的题.1.若a>0,b>0,且2a+b=1,求S=2√ab-4a^2-b^2的最大值.2.求S=1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+……+1/[n(n+1)(n+2)]的值.3.实数x、y满足y+x^2=0,0√代表根号,^2代表平方,*代表乘以,log(a)2代表以a
1.我们可以变换一下,S=2√ab-4a^2-b^2=2√ab+4ab-1
令x=√ab,得S=2x+4x^2-1,求出来x的取值范围就可以了.由2a+b=1,得b=1-2a,所以x^2=a(1-2a),求出x^2的取值范围是(0,1/4],所以0
符号不懂
第一二问“晴天有我”都答了,没问题的
第三问的解答如下:
首先(x-1/2)^2>=0 =>x-x^2<1/4 =>a^(x-x^2)>=a^(1/4)
=>a^x*a^y=a^x*a(-x^2)>=a^(1/4)
sqrt(a^x*a^y)>=a^(1/8)
又由均值不等式 =>sq...
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第一二问“晴天有我”都答了,没问题的
第三问的解答如下:
首先(x-1/2)^2>=0 =>x-x^2<1/4 =>a^(x-x^2)>=a^(1/4)
=>a^x*a^y=a^x*a(-x^2)>=a^(1/4)
sqrt(a^x*a^y)>=a^(1/8)
又由均值不等式 =>sqrt(a^x*a^y)<=1/2(a^x+a^y)
=>a^x+a^y >=2*a^(1/8)
两边对a取对数,由于0 =log(a)2+1/8
证毕
当且仅当x=1/2 y=-1/4时等号成立
祝好~
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