Các câu hỏi tương tự
cho a,b,c la 3 so khac 0 va a+b+c=0 chung minh rang 1/a^2+b^2-c^2+1/b^2+c^2-a^2+1/c^2+a^2-b^2=0
cho a+b+c=1 va 1/a+1/b+1/c=0.Chung minh rang : a^2+b^2+c^2=0
Cho a b c la cac so thuc. A+b+c=1 va 1/a+1/b+1/c=0. Chung minh A mu 2+ b mu 2+c mu 2=1
Cho a. b, c > 0 . Chung minh rang : 4/a + 5/b + 3/c >= 4(3/a+b + 2/b+c + 1/c+a)
a+b+c=0 va 1/a+1/b+1/c=1 chung minh a^2+b^2+c^2=1
cho 3 so a,b,c khac 0 va (a+b+c)^2=a^2+b^2+c^2 . chung minh \(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}=3abc\)
cho a,b,c >0 thoa man a+b+c=3.chung minh (a^2+bc)/(b+ca) + (b^2+ca)/(c+ab) + (c^2+ab)/(a+bc) ≥ 3
cho a+b+c=1 chung minh (a+bc)(b+ac)(c+ab)=(a+b)^2(a+c)^2(b+c)^2
Cho a, b, c >0. Chung minh \(\frac{a^2}{b^3}+\frac{b^2}{c^3}+\frac{c^2}{a^3}>\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)