cho so nguyen to p va cac so duong x,y thoa man 4x^2-3xy-y^2-p(3x+2y)=2p^2 CHUNG MINH RANG 5x-1 la so chinh phuong
cho 3 so nguyen x,y,z thoa man x+y+z=0 chung minh rang x^3+y^3+z^3= 3xyz
chung minh rang khong co gia tri nguyen nao cua x,y,z thoa man :x^3+y^3+x^3=x+y+z+2009
cho x,y,z>0 thoa man x+y+z<=1 chung minh rang 17(x+y+z)+2(1/x+1/y+1/z)=>35
cho x,y,z duong thoa man xy+yz+xz>=3
Chứng minh \(\frac{x^4}{y+3z}+\frac{y^2}{z+3x}+\frac{z^4}{x+3y}>=\frac{3}{4}\)
a) Goi a,b,c la do dai ba canh cua mot tam giac thoa man a3 + b3 + c3 = 3abc. Chung minh do la tam giac deu
b) Cho x y z duong va x+y+z = 1. Chung minh \(\frac{1}{x^2+2yz}+\frac{1}{y^2+2xz}+\frac{1}{z^2+2xy}\ge9\)
Cho x,y,z la cac so thuc khac 0. Thoa man : z2+z(xy-xz-yz)=0
Chung minh rang x2+(x+2y-z)2 / y2+(2x+y-z)2 = x+2y-z / 2x+y-z
cho x,y,z duong va x+y+z=1. chung minh rang 1/x^2+2yz+1/y^2+2xz+1/z^2+2xy>=9
thank, giup minh mik cho 3 tick
cho x,y la 2 so khac nhau thoa man x+y=x^5+y^5 . chung minh x,y la 2 so doi nhau
