Violympic toán 8
Các câu hỏi tương tự
Cho biết: \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=2\); \(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=2\). CMR: a+b+c=abc
Cho: \(\left(a+b+c\right)^2=a^2+b^2+c^2\) và a, b, c khác 0. CMR: \(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\)
Cho: \(\left(a+b+c\right)^2=a^2+b^2+c^2\) và a,b, c khác 0. CMR: \(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\)
cho các số a,b,c khac 0, thỏa mãn a+b+c=abc va \(\dfrac{1}{a}\)+\(\dfrac{1}{b}\)+\(\dfrac{1}{c}\)=2
CMR: \(\dfrac{1}{a^2}\)+\(\dfrac{1}{b^2}\)+\(\dfrac{1}{c^2}\)=2
Cho a,b,c > 0 . CMR :
a) \(\dfrac{a}{b^2}+\dfrac{b}{c^2}+\dfrac{c}{a^2}\) ≥ \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Cho \(a;b;c>0\). CMR:
\(\dfrac{a+b}{a^2+bc}+\dfrac{b+c}{b^2+ca}+\dfrac{c+a}{c^2+ab}\le\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Cho a,b,c khác 0 thỏa mãn a+b+c=abc và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=2\) Tính \(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}\)
CMR nếu \(\left(a^2-bc\right).\left(b-abc\right)=\left(b^2-ac\right).\left(a-abc\right)\) và các số a, b, c, a-b khác 0 thì \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=a+b+c\)
Cho a, b, c >0 thỏa mãn: abc=1. CM: \(\dfrac{1}{a^2-ab+b^2}+\dfrac{1}{b^2-bc+c^2}+\dfrac{1}{c^2-ac+a^2}\le a+b+c\)