Cho x^2-y=A: y^2-Z= B;z^2-x=C với A,B,C là hằng số.CMR gtrij cua bthuc tren ko phu thuoc vao bien xyz
chung minh bieu thuc ko phu thuoc vao gia tri cua bien
A=(2x+5).(4x^2-6x+9)-2(4x.3-1)
B=(x+3)^3-(x+9).(x^2+27)
cho a+b+c=0.P=a^2+b^2+c^2. Tim min P
thanks b nao co cau tl hay va dung nhat nke
cho a,b,c khac nhau doi mot va 1/a+1/b+1/c=0.rut gon cac bieu thuc
N=bc/a^2+2bc+CA/B^2+2AC+AB/C^2+2AB
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
Giai va bien luan cac phuong trinh sau:
1. \(\frac{a+b-x}{c}+\frac{a+c-x}{b}+\frac{b+c-x}{a}+\frac{4x}{a+b+c}=1\)
(an x) voi dk; a,b,b khac 0 va a+b+c khac 0
2.\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
(an x) voi dk: a,b,c khac 0
3, \(\frac{mx+3}{6}+\frac{m^2-1}{2}=\frac{x+5}{10}+\frac{2}{5}\left(x+m^2+1\right)\)
(an x)
Cho a,b,c là cac số thực khác 0 , tổng bằng 0
Tinh S = 1/b^2+c^2-a^2 + 1/c^2+ a^2 -b^2 + 1/a^2 +b^2 -c^2
Cho cac so thuc phan a,b,c khac nhau doi mot va thoa man a^2-b=b^2-c=c^2-a . CMR (a+b+1)()b+c+1(c+a+1)=-1- de hsg tinh mon toan 9 nam 2012