Tìm x \(\in\) Z biết:
3) \(\dfrac{1-18x}{2017}+\dfrac{2-18x}{2016}=\dfrac{3-18x}{2015}+\dfrac{4-18x}{2014}\)
Tìm các số x,y,z biết:
a.9x=5y=15z và -x+y-z=11
b.\(\dfrac{3}{7}x=\dfrac{8}{13}y=\dfrac{6}{19}z\) và 2x-y-z=-6
c.\(\dfrac{x}{8}=\dfrac{y}{3}=\dfrac{z}{10}\) và xy+yz+zx=1206
d.\(\dfrac{x}{4}=\dfrac{2y}{5}=\dfrac{5z}{6}\)và x2-3y2+2z2=325
c.\(\dfrac{18x-27y}{100}=\dfrac{27y-24z}{101}=\dfrac{24z-18x}{102}\) và x+y+z=116
a)
Ta có: \(9x=5y=15z\Rightarrow\dfrac{9x}{45}=\dfrac{5y}{45}=\dfrac{15z}{45}\Rightarrow\dfrac{x}{5}=\dfrac{y}{9}=\dfrac{z}{3}\Rightarrow\dfrac{-x}{-5}=\dfrac{y}{9}=\dfrac{z}{3}_{\left(1\right)}\)
và \(-x+y-z=11_{\left(2\right)}.\)
Từ \(_{\left(1\right)}\) và \(_{\left(2\right)}\), kết hợp tính chất dãy tỉ só bằng nhau có:
\(\dfrac{-x}{-5}=\dfrac{y}{9}=\dfrac{z}{3}=\dfrac{-x+y-z}{-5+9-3}=\dfrac{11}{1}=11.\)
Từ đó: \(\left\{{}\begin{matrix}\dfrac{-x}{-5}=11\Rightarrow-x=-55\Rightarrow x=55.\\\dfrac{y}{9}=11\Rightarrow y=99.\\\dfrac{z}{3}=11\Rightarrow z=33.\end{matrix}\right.\)
Vậy.....
b); c); d); e) làm tương tự.
Tính đạo hàm của các hàm số sau:
a) y=\(\dfrac{3x^2-18x-2}{1-2x}-\dfrac{2x-3}{x+4}\)
b) y=\(-\dfrac{\sin x}{3\cos^3x}+\dfrac{4}{3}\tan x\)
1) Rút gọn bt:
(x+y+z)3+(x-y-z)3+(y-x-z)3+(z-y-x)3
2)Tìm x,y,z t/m: 9x2+y2+2z2-18x+4z-6y+20=0
3)Cho \(\dfrac{x}{a}+\dfrac{y}{b}+\dfrac{z}{c}\)=1 và \(\dfrac{a}{x}+\dfrac{b}{y}+\dfrac{c}{z}\)=0 . CMR:
\(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}\)=1
Cho 2 số dương x,y thỏa mãn x+y≥5
Tìm GTNN của biểu thức
A= \(18x+\dfrac{56}{3}y+\dfrac{4}{x}+\dfrac{15}{y}\)
Min của A là 99 khi (x;y)=(2;3).
Chúc abh học tốt.
\(A=\left(x+\dfrac{4}{x}\right)+5\left(\dfrac{y}{3}+\dfrac{3}{y}\right)+17\left(x+y\right)\)
\(A\ge2\sqrt{\dfrac{4x}{x}}+5.2\sqrt{\dfrac{3y}{3y}}+17.5=99\)
Dấu "=" xảy ra khi \(\left(x;y\right)=\left(2;3\right)\)
a, \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
b, \(\dfrac{x+2}{x-3}-\dfrac{x^2+6}{x^2-3x}\)
c, \(\dfrac{1}{9x-18}+\dfrac{16-7x}{72-18x}+\dfrac{5}{12x-24}\)
a.\(\dfrac{3}{2\left(x+3\right)}-\dfrac{x-6}{2x\left(x+3\right)}=\dfrac{3x-x+6}{2x\left(x+3\right)}=\dfrac{2x+6}{2x\left(x+3\right)}=\dfrac{1}{x}\)
M= \(\dfrac{3}{2}\sqrt{32x}-\dfrac{1}{3}\sqrt{18x}+\dfrac{2}{5}\sqrt{50x}-4\sqrt{2x}\) (x lớn hơn hoặc bằng 0)
giải chi tiết giúp mk vớiiiii ạ
\(M=\dfrac{3}{2}\cdot4\sqrt{2x}-\dfrac{1}{3}\cdot3\sqrt{2x}+\dfrac{2}{5}\cdot5\sqrt{2x}-4\sqrt{2x}=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)
Rút gọn biểu thức
M=\(\dfrac{3}{2}\sqrt{32x}-\dfrac{1}{3}\sqrt{18x}+\dfrac{2}{5}\sqrt{50x}-4\sqrt{2x}\) (x ≥ 0)
giải chi tiết giúp mk vớiiiiii ạ
\(M=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)
Thuc hien phep tinh :\(\dfrac{18x}{x^3-9x}-\dfrac{2-x}{x+3}+\dfrac{3}{3-x}\)
\(\dfrac{18x}{x^3-9x}-\dfrac{2-x}{x+3}+\dfrac{3}{3-x}\)
=\(\dfrac{18x}{x\left(x^2-9\right)}-\dfrac{\left(2-x\right)\left(x-3\right)x}{\left(x+3\right)\left(x-3\right)x}-\dfrac{3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)x}\)
=\(\dfrac{18x-\left(2-x\right)\left(x-3\right)x-3x\left(x+3\right)}{x\left(x+3\right)\left(x-3\right)}\)
=\(\dfrac{18x-\left(2x-6-x^2+3x\right)x-3x^2-9x}{x\left(x+3\right)\left(x-3\right)}\)
=\(\dfrac{18x-2x^2+6x+x^3-3x^2-3x^2-9x}{x\left(x+3\right)\left(x-3\right)}\)
=\(\dfrac{x^3-8x^2+15x}{x\left(x-3\right)\left(x+3\right)}\)
=\(\dfrac{x\left(x^2-8x+15\right)}{x\left(x-3\right)\left(x+3\right)}\)
=\(\dfrac{x^2-3x-5x+15}{x\left(x-3\right)\left(x+3\right)}\)
=\(\dfrac{x\left(x-3\right)-5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)
=\(\dfrac{\left(x-3\right)\left(x-5\right)}{\left(x-3\right)\left(x+3\right)}\)
=\(\dfrac{\left(x-5\right)}{x+3}\)
GHPT sau: \(\left\{{}\begin{matrix}\dfrac{25}{9}+\sqrt{9x^2-4}=\dfrac{1}{9}\left(\dfrac{2}{x}+\dfrac{18x}{y^2-2y+2}+25y\right)\\7x^3+y^3+3xy\left(x-y\right)-12x^2+6x=1\end{matrix}\right.\)