tim gtnn
cho a+b+c=6
tim gtnn
A=(a+1)/a+(b+1)/b+(c+4)/c
XL
Những câu hỏi liên quan
1, tim GTLN cua A=13/(x+5)^2+7
2, tim GTNN cua B=|x+2017|+(y+3)^2+2017
3, cho a-1/2=b+3/4=c-5/6 va 5a-3b-4c=46. Tim a,b,c.
cho a,b,c >0 va a+b+c>=6.tim GTNN cua A= 5a+6b+7c+1/a+8/b+27./c
Áp dụng BĐT AM-GM ta có:
\(A=5a+6b+7c+\frac{1}{a}+\frac{8}{b}+\frac{27}{c}\)
\(=4\left(a+b+c\right)+\left(\frac{1}{a}+a\right)+\left(\frac{8}{b}+2b\right)+\left(\frac{27}{c}+3c\right)\)
\(\ge4\cdot6+2\sqrt{\frac{1}{a}\cdot a}+2\sqrt{\frac{8}{b}\cdot2b}+2\sqrt{\frac{27}{c}\cdot3c}\)
\(\ge24+2+2\cdot4+2\cdot9=52\)
Xảy ra khi \(\frac{1}{a}=a;\frac{8}{b}=2b;\frac{27}{c}=3c\Rightarrow a=1;b=2;c=3\)
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cho a,b,c>0;a+b+c>=1: tim GTNN: √(a²+1/ a²)+√(b²+1/b²)+√(c²+1/c²)
Cho a+b+c=1
a, b, c>0
Tim gtnn (1+a)(1+b)(1+c)/(1-a)(1-b)(1-c)
cho a,b,c >0 va 1/a+1/c=2/b
Tim GTNN A=(a+b)/(2a-b) + (b+c)/(2c-b)
a+b+c=6 tim GTNN a^2/(a+b) + b^2/(c+a) + c^2/(b+c)
\(A=\frac{a^2}{a+b}+\frac{b^2}{c+a}+\frac{c^2}{b+c}\ge\frac{\left(a+b+c\right)^2}{2\left(a+b+c\right)}=\frac{a+b+c}{2}=\frac{6}{2}=3..\)
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cho 3 so thuc duong a, b, c thoa man 1/a+1/c=2/b. tim GTNN cua (a+b)/(2a-b)+(b+c)(/2c-b)
\(\frac{1}{a}+\frac{1}{c}=\frac{2}{b}\Leftrightarrow b=\frac{2ac}{a+c}\)
\(P=\frac{a+b}{2a-b}+\frac{b+c}{2c-b}=\frac{a+\frac{2ac}{a+c}}{2a-\frac{2ac}{a+c}}+\frac{\frac{2ac}{a+c}+c}{2c-\frac{2ac}{a+c}}=\frac{a+3c}{2a}+\frac{3a+c}{2c}=1+\frac{3}{2}\left(\frac{a}{c}+\frac{c}{a}\right)\ge4\)
Dấu "=" xảy ra khi \(a=b=c\)
cho a,b,c,d,e >0 có tổng =4.Tim GTNN cua P=((a+b+c+d)(a+b+c)(a+b))/abcde
Nhân P với 4. Do 4=a+b+c+d+e
Áp dụng \(\left(x+y\right)^2\ge4xy\)
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cho a,b,c la cac so thoa man (a+1)^2+(b+2)^2+(c+3)2<2010.tim GTNN cua bieu thuc A=ab+b(c-1)+c(a-2)