Tìm các số A , B , C để có
a) \(\frac{x^2-x+2}{\left(x-1\right)^3}=\frac{A}{\left(x-1\right)^3}+\frac{B}{\left(x-1\right)^2}+\frac{C}{x-1}\)
b) \(\frac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}\)
Tìm các sô A; B; C để có :
a) \(\frac{x^2-x+2}{\left(x-1\right)^3}=\frac{A}{\left(x-1\right)^3}+\frac{B}{\left(x-1\right)^2}+\frac{C}{x-1}\)
b) \(\frac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}\)
Tính A+B+C biết A=\(\frac{1}{\left(x+y\right)^3}.\left(\frac{1}{x^4}-\frac{1}{y^4}\right)\) , B=\(\frac{2}{\left(x+y\right)^4}.\left(\frac{1}{x^3}-\frac{1}{y^3}\right)\) ,C=\(\frac{1}{\left(x+y\right)^5}.\left(\frac{1}{x^2}-\frac{1}{y^2}\right)\)
\(\frac{x^2-x+2}{\left(x-1\right)^3}=\frac{A}{\left(x-1\right)^3}+\frac{B}{\left(x-1\right)^2}+\frac{C}{x-1}\)
Tìm A,B,C?
Cho \(A=\frac{1}{\left(x+y\right)^3}\left(\frac{1}{x^4}-\frac{1}{y^4}\right);B=\frac{1}{\left(x+y\right)^4}\left(\frac{1}{x^3}-\frac{1}{y^3}\right);C=\frac{1}{\left(x+y\right)^5}\left(\frac{1}{x^2}-\frac{1}{y^2}\right)\)
a) Rút gọn tổng A+B+C
b) Tính tổng A+B+C tại x=2016;y=2017
1)\(\frac{1}{\left(a-b\right)\left(a-c\right)}+\frac{1}{\left(b-c\right)\left(b-a\right)}+\frac{1}{\left(c-a\right)\left(c-b\right)}\)
2)\(\frac{a^2}{\left(a-b\right)\left(a-c\right)}+\frac{b^2}{\left(b-c\right)\left(b-a\right)}\frac{c^2}{\left(c-a\right)\left(c-b\right)}\)
3)\(\frac{1}{x^2+3x+2}+\frac{2x}{x^3+4x^2+4x}+\frac{1}{x^2+5x+6}\)
Tìm các số a,b,c thỏa mãn :
a) \(\frac{\text{x^2}-x+2}{\text{ }\left(x-1\right)^3}=\frac{A}{\left(x-1\right)^3}+\frac{B}{\left(x-1\right)^2}+\frac{C}{x-1}\) b)\(\frac{x^2+2x-1}{\left(x-1\right)\left(x^2+1\right)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}\)
:| Giúp tớ với
1.tìm các nghiem nguyen cua phuong trinh: 54x^3+1=y^3
2.cho x+y=1 và xy khac 0.chung mih \(\frac{x}{y^3-1}+\frac{y}{x^3-1}+\frac{2\left(x-y\right)}{x^2y^2+3}=0\)
3.cho a,b,c la cac so thuc duong.chung minh :\(\left(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\right)^2+\frac{14abc}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\ge4\)
Bài 1: Cho a,b,c đôi một khác nhau. CMR:
\(\frac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\frac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}+\frac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}=1\)=1
Bài 2: CMR: nếu \(\frac{1}{x}-\frac{1}{y}-\frac{1}{z}=1\)và x=y+z thì:
\(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=1\)