Các câu hỏi tương tự
Cho a,b,c khác 0 t/m \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\) và \(\frac{2}{bc}-\frac{1}{a^2}=1\)
Tính \(P=\left(a-2b+4c\right)^{2019}\)
Cho a,b,c khác 0 thỏa mãn: \(\frac{1}{a}+\frac{1}{2b}+\frac{1}{3c}=0\). Tính
\(A=\frac{bc}{a^2}+\frac{ac}{8b^2}+\frac{ab}{27c^2}\)
Chứng minh :
A = \(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2018^2}+\frac{1}{2019^2}}+\sqrt{1+\frac{1}{2019^2}+\frac{1}{2020^2}}\)
là 1 số hữu tỉ .
Cho \(f\left(x\right)=\frac{x^3}{1-3x+3x^2}.\) Tính \(A=f\left(\frac{1}{2020}\right)+f\left(\frac{2}{2020}\right)+...+f\left(\frac{2018}{2020}\right)+f\left(\frac{2019}{2020}\right).\)
Cho \(f\left(x\right)=\frac{x^3}{1-3x+3x^2}.\) Tính \(A=f\left(\frac{1}{2020}\right)+f\left(\frac{2}{2020}\right)+...+f\left(\frac{2018}{2020}\right)+f\left(\frac{2019}{2020}\right).\)
M=\(\frac{a^2+a-6}{a+1}\)+\(\frac{2b^2+2b-3}{b+1}\)+\(\frac{3c^2+3c-2}{c+1}\)
cho a,b,c>0 và a+2b+3c=6 tìm max M
cho a,b,c thỏa mãn: \(\frac{2}{\left(x+1\right)\left(x-1\right)}=\frac{ax+b}{x^2+1}+\frac{c}{x-1}\)
Tính giá trị biểu thức : A=\(A=\frac{a^{2017}+b^{2018}+c^{2019}}{a^{2017}\times b^{2018}\times c^{2019}}\)
Cho a,b,c>0 ; abc=\(\frac{1}{6}\).C/m:\(3+\frac{a}{2b}+\frac{2b}{3c}+\frac{3c}{a}\ge a+2b+3c+\frac{1}{a}+\frac{1}{2b}+\frac{1}{3c}\)
Cho a,b,c thỏa mãn\(\frac{2}{\left(x^2+1\right)\left(x-1\right)}=\frac{ax+b}{x^2+1}+\frac{c}{x-1}\) .
Tính M=\(\frac{a^{2017}+b^{2018}+c^{2918}}{a^{2017}b^{2018}c^{2019}}\)