cho M =(-a +b)-(b+c-a)+(c-a) .Trong do b,c la so nguyen con a la so nguyen am.Chung minh rang bieu thuc M luon luon duong

cho P=a/a+b+b/b+c+c/c+a voi a,b,c la cac so nguyen duong .Hoi P có phai số tự nhiên ko

Cho a,b,c nguyen duong sao cho a^2/b, b^2/c, c^2/a la cac so nguyen to. cmr a=b=c

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 M =(-a+b)-(b+c-a)+(c-a).Trong do b,c la so nguyen am hoac duong.a la so nguyen am.Chung minh M>0

cho a/b<c/d, a, b, c, d la nhung so nguyen duong. hay so sanh a/b, c/d voi a-c/b-d

Cho so huu ti x=\(\frac{a-3}{2}\)

Voi gia tri nao cua xthi

a ) la so nguyen duong

b) la so nguyen am

c) x ko la duong cung ko am

cho x,y,z la cac so nguyen duong va x+y+z la so le, cac so thuc a,b,c thoa man (a-b)/x=(b-c)/y=(a-c)/z. chung minh rang a=b=c

Cho a, b, c, d la cac so nguyen duong thoa man a + b=c + d= 25

Tim GTLN cua M = \(\frac{c}{b}\)+ \(\frac{d}{a}\)