cho a,b,c, la cac so duong thoa man a+b+c=1, c/m :1/a+1/b+1/c>=9
cho cac so duong a,b,bc thoa man a+b+c=1/abc .chung ming (a+b)(a+c)>=2
cho cac so nguyen duong a,b,c thoa man :(a,b,c)=1;ab=c(a+b).Cm a+b la so chinh phuong
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 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
\(\frac{1}{a^3\left(b+c\right)}+\frac{1}{b^3\left(c+a\right)}+\frac{1}{c^3\left(a+b\right)}\ge\frac{3}{2}\)
chung minh rang voi a,b,c la cac so duong ,ta co (a+b+c)(1/a+1/b+1/c)>=9
Cho cac so nguyen duong a b c thoa man
(a+1)^3+(b+2)^3+(c+3)^3=3(a+1)(b+2)(c+3)
cho cac so duong a,b,c thoa man (a^2+b^2+c^2)^2>2*(a^4+b^4+c^4)
cm rang a,b,c la do dai ba canh cua tam giac.
