Violympic toán 9
Các câu hỏi tương tự
Cho ba số thực a, b, c. Chứng minh:
\(\frac{9a}{b+c}+\frac{25b}{c+a}+\frac{64c}{a+b}>30\)
Cho a,b,c \(\ge\)và a+b+c =1
CMR: \(\frac{1}{a^2+b^2+c^2}+\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\ge30\)
CMR \(\left(a+\frac{1}{b}\right)\left(b+\frac{1}{c}\right)\left(c+\frac{1}{a}\right)>=\left(\frac{10}{3}\right)^2\) voi a,b,c >0 va a+b+c=1
Bài 1: Cho a,b,c \(\ge\)0. CMR: \(\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}\ge6\)
Bài 2: Cho a,b,c \(\ge\)0. CMR: \(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge\frac{3}{2}\)
(4)Bài 1:Với forall ab0. CMR: a+ frac{1}{bleft(a-bright)}ge3
(7) Bài 2: Cho a,b,c ne 0 .CMR: frac{a^2}{b^2}+frac{b^2}{c^2}+frac{c^2}{a^2}gefrac{b}{a}+frac{c}{b}+frac{a}{c}
(8) Bài 3: Cho a,b,c0 thõa mãn abc1
CMR: frac{b+c}{sqrt{a}}+frac{c+a}{sqrt{b}}+frac{a+b}{sqrt{c}}gesqrt{a}+sqrt{b}+sqrt{c}+3
Đọc tiếp
(4)Bài 1:Với \(\forall\) a>b>0. CMR: a+ \(\frac{1}{b\left(a-b\right)}\ge3\)
(7) Bài 2: Cho a,b,c \(\ne\) 0 .CMR: \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{b}{a}+\frac{c}{b}+\frac{a}{c}\)
(8) Bài 3: Cho a,b,c>0 thõa mãn abc=1
CMR: \(\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}+3\)
Cho a,b,c>0 CMR \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{a+b}{b+c}+\frac{b+c}{a+b}+1\)
cho a, b, c >0. cmr: \(\frac{a}{c}+\frac{b}{a}+\frac{c}{b}\ge\frac{9}{a+b+c}\)
Cho các số thực a, b, c khác 0 thỏa mãn a + b + c = 0. CMR: \(\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}=\left|\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right|\)
cho a,b,c>0 . CMR: \(\frac{b}{a+3b}+\frac{c}{b+3c}+\frac{a}{c+3a}\le\frac{a+b+c}{4}\)