so cac cap so tu nhien (x;y) thoa man dieu kien: (x+3)(y+2)=20

tim cac so nguyen x,y,z thoa man dieu kien sau

x^2=y-1

y^2=z-1

z^2=x-1

cho x;y;z;t la 4 so khac 0 va thoa man cac dieu kien sau:

^{y^2=xz, z^2=yt, vay^3+z^3+t^3kac 0chung minh rang:} 

(y^3+z^3+x^3)/y^3+z^3+t^3=x/t

Cho x,y, z la cac so duong thoa man dieu kien x+y+z=a

tim GTNN : Q=\(\left(1+\dfrac{a}{x}\right)\left(1+\dfrac{a}{y}\right)\left(1+\dfrac{a}{z}\right)\)

cho cac so x,y,z va x+y+z khac 0 thoa man dieu kien 

\(\frac{x+2y}{x+2y-z}+\frac{y+2z}{y+2z-x}+\frac{z+2x}{z+2x-+y}\)

tinh gt bieu thuc \(T=\frac{x^2+y^2}{xy}+\frac{y^2+z^2}{yz}+\frac{z^2+x^2}{zx}\)

Cho x y z la cac so huu ti doi mot khac nhau va khac khong thoa man x+1/y=y+1/z=z+1/x    Chung minh xyz=1 hoac xyz=-1

Cho x,y,z la cac so duong thoa man dieu kien x+y+z > hoac = 12

GTNN: P =\(\dfrac{x}{\sqrt{y}}+\dfrac{y}{\sqrt{z}}+\dfrac{z}{\sqrt{x}}\)

biet 4 so tu nhien lien tiep thoa man dieu kien so lien tiep khac nhau 15 don vi va tong la 2170 tim so lon nhat

tim cac so nguyen to  x y z thoa man 3(x+y+z)=xyz