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

\(P=\frac{2+a}{\sqrt{2-a}}+\frac{2+b}{\sqrt{2-b}}\)

Cho a, b, c, d la cac so nguyen duong  thoa man a²+b²=b²+d². CM a+b+c+d la hop so

cho a, b, c, d la 4 so nguyen duong thoa man: b= \(\frac{a+c}{2}va\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)

chung minh: \(\frac{a}{b}=\frac{c}{d}\)

cho cac so nguyen duong a,b,c , d thoa man ab=cd. Chung minh:

A=\(a^{2008}+b^{2008}+c^{2008}+d^{2008}\) la hop so

cho a,b,c,d la cac so nguyen duong doi 1 khac nhau thoa man a/a+b  +   b/b+c   +  c/c+d  + d/d+a   =2

CMR abcd la 1 so chinh phuong

Cho a,b,c la cac so nguyen duong thoa man: abc=1. CMR
\(\frac{1}{a^3\left(b+c\right)}+\frac{1}{b^3\left(c+a\right)}+\frac{1}{c^3\left(a+b\right)}\ge\frac{3}{2}\)

cho a,b,c la cac so thuc duong thoa man a+b+c=3. tim gia tri nho nhat cua

P=\(\frac{a}{a^3+b^2+c}+\frac{b}{b^3+c^2+a}+\frac{c}{c^3+a^2+b}\)

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