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\(\frac{x}{2}+\frac{y}{3}=\frac{x+y}{2+3}=>\frac{3x}{6}+\frac{2y}{6}=\frac{x+y}{5}\)
Bài 1 sai đề
Bài 2:
Có: \(\frac{1}{x}=\frac{y}{2}-1\)
\(\Rightarrow\frac{1}{x}=\frac{y-2}{2}\)
\(\Rightarrow x\left(y-2\right)=2\)
Bài2(tiếp): Vì x, y nguyên dương nên x=2;y-2=1 hoặc x=1; y-2=2
Xét: y-2=1
y=3
Suy ra: cặp (x;y) TM là (2:3)
Xét: y-2=2
y=4
Suy ra: cặp (x,y) TM là (1;4)
Vậy cặp số (x,y) TM là (2;3); (1;4)
\(\frac{x-2}{27}+\frac{x-3}{26}+\frac{x-4}{25}+\frac{x-5}{24}+\frac{x-44}{5}=1\)
\(\Leftrightarrow\left(\frac{x-2}{27}-1\right)+\left(\frac{x-3}{26}-1\right)+\left(\frac{x-4}{25}-1\right)+\left(\frac{x-5}{24}-1\right)\)\(+\left(\frac{x-44}{5}+3\right)=1-1\)
\(\Leftrightarrow\frac{x-29}{27}+\frac{x-29}{26}+\frac{x-29}{25}+\frac{x-29}{24}\)\(+\frac{x-29}{5}=0\)
\(\Leftrightarrow\left(x-29\right)\left(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\right)=0\)
Mà \(\frac{1}{27}+\frac{1}{26}+\frac{1}{25}+\frac{1}{24}+\frac{1}{5}\ne0\)
=> x - 29 = 0
=> x = 29.
Vi vai tro cua x,y,z,t la binh dang nen gia su
\(x\le y\le z\le t\)
=> \(\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}+\frac{1}{t^2}\le\frac{1}{x^2}+\frac{1}{x^2}+\frac{1}{x^2}+\frac{1}{x^2}\)
\(\Rightarrow1\le\frac{4}{x^2}\Rightarrow\)\(\frac{4}{4}\le\frac{4}{x^2}\)\(\Rightarrow x^2\le4\)\(\Rightarrow x^2\in\left\{1;4\right\}\)
\(+)\)\(x^2=1\)\(\Rightarrow\)\(\frac{1}{1}+\frac{1}{y^2}+\frac{1}{z^2}+\frac{1}{t^2}=1\)\(\Rightarrow\)\(\frac{1}{y^2}+\frac{1}{z^2}+\frac{1}{t^2}=0\)(loai )
+) \(x^2=4\Rightarrow\)\(\frac{1}{4}+\frac{1}{y^2}+\frac{1}{z^2}+\frac{1}{t^2}=1\Rightarrow\)\(\frac{1}{y^2}+\frac{1}{z^2}+\frac{1}{t^2}=\frac{3}{4}\le\frac{1}{y^2}+\frac{1}{y^2}+\frac{1}{y^2}\)
\(\Rightarrow\)\(\frac{3}{4}\le\frac{3}{y^2}\)\(\Rightarrow\)\(y^2\le4\)\(\Rightarrow\)\(y^2\in\left\{1;4\right\}\)
+) \(y^2=1\Rightarrow\)\(\frac{1}{1}+\frac{1}{z^2}+\frac{1}{t^2}=1\)\(\Rightarrow\)\(\frac{1}{z^2}+\frac{1}{t^2}=0\)(loai)
+) \(y^2=4\Rightarrow\)\(\frac{1}{4}+\frac{1}{z^2}+\frac{1}{t^2}=1\)\(\Rightarrow\)\(\frac{1}{z^2}+\frac{1}{t^2}=\frac{3}{4}\le\frac{1}{z^2}+\frac{1}{z^2}\)\(\Rightarrow\)\(\frac{3}{4}\le\frac{2}{z^2}\)
\(\Rightarrow\)\(\frac{6}{8}\le\frac{6}{3z^2}\)\(\Rightarrow\)\(3z^2\le8\)\(\Rightarrow\)\(z^2\le2\)\(\Rightarrow\)\(z^2=1\)
den day minh chiu
Ta có
\(\begin{cases}\left|x-\frac{1}{2}\right|\ge0\\\left|y+\frac{3}{2}\right|\ge0\\\left|x+y-z-\frac{1}{2}\right|\ge0\end{cases}\)
Maf \(\left|x-\frac{1}{2}\right|+\left|y+\frac{3}{2}\right|+\left|x+y-z-\frac{1}{2}\right|=0\)
\(\Rightarrow\begin{cases}x-\frac{1}{2}=0\\y+\frac{3}{2}=0\\x+y-z-\frac{1}{2}=0\end{cases}\)
\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\x+y-z=\frac{1}{2}\end{cases}\)
\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\\frac{1}{2}-\frac{3}{2}-z=\frac{1}{2}\end{cases}\)
\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\-z=\frac{3}{2}\end{cases}\)
\(\Rightarrow\begin{cases}x=\frac{1}{2}\\y=-\frac{3}{2}\\z=-\frac{3}{2}\end{cases}\)
a) Ta có : \(\frac{x}{3}-\frac{4}{y}=\frac{1}{5}\)
\(\Rightarrow\frac{x}{3}-\frac{1}{5}=\frac{4}{y}\)
\(\Rightarrow\frac{x.5}{15}-\frac{3}{15}=\frac{4}{y}\)
\(\Rightarrow\frac{x.5-3}{15}=\frac{4}{y}\)
\(\Rightarrow\left(x.5-3\right).y=15.4\)
\(\Rightarrow x.5.y-3.5=60\)
\(\Rightarrow xy5-15=60\)
\(\Rightarrow xy5=60+15\)
\(\Rightarrow xy5=75\)
\(\Rightarrow xy=75\div5\)
\(\Rightarrow xy=15\)
\(\Rightarrow xy=1.15=3.5=\left(-15\right)\left(-1\right)=\left(-3\right)\left(-5\right)=\left(-5\right)\left(-3\right)=\left(-1\right)\left(-15\right)=5.3=15.1\)
Do đó x = 1 thì y = 15
x = 3 thì y =5
x = -15 thì y = -1
x = -3 thì y = -5
x = -5 thì y = -3
x = -1 thì y = -15
x = 5 thì y = 3
x = 15 thì y = 1