???? là sao vừa lớn vừa bằng đó
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1. Cho a,b,c,d la cac so nguyen thoa man \(a^2=b^2+c^2+d^2\)
chung minh rang a.b.c.d + 2015 viet duoc duoi dang hieu cua 2 so chinh phuong.
2. Cho a,b la cac so duong thoa man dieu kien a+b=1. tim gia tri nho nhat cua bieu thuc
\(P=\frac{2+a}{\sqrt{2-a}}+\frac{2+b}{\sqrt{2-b}}\)
1. Cho a,b la 2 so duong thoa a+b<=1.chung minh rang \(6b+\frac{1}{3a}+\frac{4}{b}\ge11\).
2. cho a,b,c la cac so nguyen duong sao cho (a-b).(a-c).(b-c)=a+b+c
a. chung minh rang a+b+c chia het cho 2
b. Tim gia tri nho nhat cua M=a+b+c
cho a,b,c la ba so thuc duong thoa man dieu kien a+b+c=1
chung minh rang P=\(\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}\le\frac{3}{2}\)
cho cac so a,b,c duong thoa man ab+bc+ca=1 chung minh : \(p=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)
cho 3 so duong a,b,c thoa man a+b+c=3
cm rang \(\frac{a}{1+b^2}+\frac{b}{1+c^2}+\frac{c}{1+a^2}>=\frac{3}{2}\)
Cho a,b.c la cac so duong va abc = 1
Chung minh rang \(\frac{1}{a^2+2b^2+3}+\frac{1}{b^2+2c^2+3}+\frac{1}{c^2+2a^2+3}\le\frac{1}{2}\)
cho a,b,c la cac so thuc duong thoa man a+b+c=3. tim gia tri nho nhat cua
P=\(\frac{a}{a^3+b^2+c}+\frac{b}{b^3+c^2+a}+\frac{c}{c^3+a^2+b}\)
Cho a,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)
Cho a,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)