Cho x, y, z thoả mãn xyz = 2023.
Chứng minh: \(\dfrac{2023x}{xy+2023x+2023}+\dfrac{y}{yz+y+2023}+\dfrac{z}{xz+z+1}=1\)
hãy tìm giá trị của x trong các biểu thức sau biết x thuộc Z : \(\dfrac{2}{x}+\dfrac{1}{y}=3\) ; \(\dfrac{2}{y}-\dfrac{1}{x}=\dfrac{8}{xy}+1\) ; \(x-\dfrac{1}{y}-\dfrac{4}{xy}=-1\) ; \(\dfrac{-3}{y}-\dfrac{12}{xy}=1\) ; \(\dfrac{x}{8}-\dfrac{1}{y}=\dfrac{1}{4}\).
help me pls!
Tìm x, y, z, t ∈ Z biết:
a, \(\dfrac{5}{x}=\dfrac{-10}{12}\) b, \(\dfrac{4}{-6}=\dfrac{x+3}{9}\) c, \(\dfrac{x-1}{25}=\dfrac{4}{x-1}\) d, \(\dfrac{x+1}{y}=\dfrac{-3}{5}\)
e, \(\dfrac{-12}{6}=\dfrac{x}{5}=\dfrac{-y}{3}=\dfrac{Z}{-17}=\dfrac{-t}{-9}\)
h, \(\dfrac{-24}{-6}=\dfrac{x}{3}=\dfrac{4}{y^2}=\dfrac{Z^3}{-2}\)
\(\dfrac{1}{x}\)+\(\dfrac{1}{y}\)+\(\dfrac{1}{z}\)=\(\dfrac{4}{5}\)timf x,y,z
Tìm x,y ϵ Z biết: \(\dfrac{5}{x}\)- \(\dfrac{y}{3}\)= \(\dfrac{1}{6}\)
a) \(\dfrac{12}{16}\) = \(\dfrac{-x}{4}\) = \(\dfrac{21}{y}\) = \(\dfrac{z}{80}\)
b) \(\dfrac{1}{3}\) x + \(\dfrac{2}{5}\) ( x - 1 ) = 0
c) ( 2x - 3 )( 6 - 2x ) = 0
d) \(\dfrac{-2}{3}\) - \(\dfrac{1}{3}\) ( 2x - 5 ) = \(\dfrac{3}{2}\)
e) 2 |\(\dfrac{1}{2}\) x - \(\dfrac{1}{3}\) | - \(\dfrac{1}{4}\)
$\dfrac{x}{2}$=$\dfrac{y}{3}$=$\dfrac{z}{5}$ và xyz = -30
Tìm các số nguyên x,y biết :
a). \(\dfrac{x}{2}\)=\(\dfrac{-5}{y}\). b). \(\dfrac{3}{x}\)=\(\dfrac{y}{4}\), trong đó x > y > 0.
c). \(\dfrac{3}{x-1}\)= y+1. d). \(\dfrac{x+2}{5}\)=\(\dfrac{1}{y}\).
Hãy tính các tổng sau:
a)\(\dfrac{1}{1\cdot3}\)+\(\dfrac{1}{3\cdot5}\)+\(\dfrac{1}{5\cdot7}\)+\(\dfrac{1}{7\cdot9}\)+\(\dfrac{1}{9\cdot11}\)=
b)\(\dfrac{1}{4\cdot7}\)+\(\dfrac{1}{7\cdot10}\)+\(\dfrac{1}{10\cdot13}\)+\(\dfrac{1}{13\cdot16}\)=
c)\(\dfrac{1}{2\cdot7}\)+\(\dfrac{1}{7\cdot12}\)+\(\dfrac{1}{12\cdot17}\)+...=