\(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\)
\(\Leftrightarrow\left(\dfrac{1}{x}\right)^3+\left(\dfrac{1}{y}\right)^3+\left(\dfrac{1}{z}\right)^3=3.\dfrac{1}{x}.\dfrac{1}{y}.\dfrac{1}{z}\)
T có: \(M=\dfrac{xyz}{x^3}+\dfrac{xyz}{y^3}+\dfrac{xyz}{z^3}\)
\(=xyz.\left(\dfrac{1}{x^3}+\dfrac{1}{y^3}+\dfrac{1}{z^3}\right)\)
\(=xyz.\dfrac{3}{xyz}=3\)
a) Rút gọn biểu thức:
\(\dfrac{x^2+x-6}{x^3-4x^2-18x+9}\)
b) Cho \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{2}=0\) (x,y,z \(\ne\)0)
Tính: \(\dfrac{yz}{x^2}+\dfrac{xz}{y^2}+\dfrac{xy}{z^2}\)
Cho \(\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=0\) khác 0. Tính P = \(\dfrac{xy}{z^2}+\dfrac{yz}{x^2}+\dfrac{zx}{y^2}\)
Cho x+y+z=0. Tính P=\(\dfrac{x^2}{yz}\)+\(\dfrac{y^2}{zx}\)+\(\dfrac{z^2}{xy}\)
cho xyz bằng 1 tính: A=\(\dfrac{x}{xy+x+1}+\dfrac{y}{yz+y+1}+\dfrac{z}{zx+z+1}\)
CHO X,Y,Z LÀ 3 số dương thoả mãn\(\dfrac{1}{x}\)+\(\dfrac{1}{y}\)+\(\dfrac{1}{z}\)=2016
tìm GTLN của P=\(\dfrac{x+y}{x^2+y^2}\)+\(\dfrac{y+z}{y^2+z^2}\)+\(\dfrac{z+x}{z^2+x^2}\)
giúp mk mình cần gấp lắm
a,\(\dfrac{x^2+y^2-xy}{x^2-y^2}:\dfrac{x^3+y^3}{x^2+y^2-2xy}\)
b,\(\dfrac{x^3y+xy^3}{x^4y}:\left(x^2+y^2\right)\)
c,\(\dfrac{x^2-xy}{y}:\dfrac{x^2-xy}{xy+y}:\dfrac{x^2-1}{x^2+y}\)
d,\(\dfrac{x^2+y}{y}:\left(\dfrac{z}{x^2}:\dfrac{xy}{x^2y}\right)\)
e,\(\dfrac{x^2+1}{x}:\dfrac{x^2+1}{x-1}:\dfrac{x^3-1}{x^2+x}:\dfrac{x^2+2x+1}{x^2+x+1}\)
g,\(\left(\dfrac{z}{x^2}:\dfrac{xy}{x^2y}\right)\dfrac{x^2+y}{y}\)
a,Tìm x,y,z thỏa mãn: \(9x^2+y^2+2x^2-18x-6y+4z+20=0\)
b, Cho \(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}=1\) và \(\dfrac{a}{x}+\dfrac{b}{y}+\dfrac{c}{z}=0\). Tính \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}\)
Cho \(P=\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}\)
và \(Q=\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}\)
Chứng minh nếu P=1 thì Q=0
Cho \(P=\dfrac{x}{y+z}+\dfrac{y}{z+x}+\dfrac{z}{x+y}\)
và \(Q=\dfrac{x^2}{y+z}+\dfrac{y^2}{z+x}+\dfrac{z^2}{x+y}\)
Chứng minh nếu P=1 thì Q=0
