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 = \(\frac{c}{b}\)+ \(\frac{d}{a}\)

B1: cho a,b,c la cac so nguyen duong

CMR:neu a /b >hoac bang c/d thi a/b > hoac bang a+c/b+d > hoac bang c/d

B2: Tim PS nho nhat khac 0 sao cho khi chia no cho 14/9 ; cho 45/27 deu duoc thuong la cac so tu nhien 

B3:CMR: 1/2^2 + 1/4^2 + 1/6^2 +....+ 1/100^2 < 1/2

cho a,b,c,x,y,z la cac so nguyen duong thoa man a^x=bc;b^y=ac;c^z=ab. chung minh xyz-x-y-z=2

cho a,b,c la cac so nguyen thoa man cac dieu kien: a+b-c=15; a-b+c=21; -a+b+c=-2015. Tim cac so nguyen do.

B1. Cho f(1)=1008,f(1)+f(2)+...+f(n)=n^2.f(n) f(n)la ham so duong

tinh f(2015)

B2 Cho cac so nguyen to q,p,r,s sao cho cac so sau deu la so nguyen to p^s+s^q,q^s+s^r,r^s+s^p

tim cac so p,q,r,s

B3 co a,b,c duong a mu 3+bmu3=c^3

so sanh a^2015+b^2015 va c^2015

cho a,b,c la cac so nguyen duong co a + b +c chia het cho 2 chung minh P=a² + b² + c² 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 x,y,z la cac so huu ti duong thoa man x+1/yz   y +1/xz  z+1/xy la cac so nguyen  tim gia tri lon nhat cua bieu thuc A=x+y^2+z^3