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y+z+1x=x+z+2y=x+y−3z=1x+y+zy+z+1x=x+z+2y=x+y−3z=1x+y+z(đk x+y+z≠0≠0
⇒y+z+1x=x+z+2y=x+y−3z=y+z+1+x+z+2+x+y−3x+y+z=2⇒y+z+1x=x+z+2y=x+y−3z=y+z+1+x+z+2+x+y−3x+y+z=2
⇒1x+y+z=2⇒x+y+z=0,5⇒1x+y+z=2⇒x+y+z=0,5
⇒y+z=0,5−x,x+z=0,5−y,x+y=0,5−z⇒y+z=0,5−x,x+z=0,5−y,x+y=0,5−z
⇒0,5−x+1x=2⇒1,5−xx=2⇒1,5−x=2x⇒3x=1,5⇒x=12⇒0,5−x+1x=2⇒1,5−xx=2⇒1,5−x=2x⇒3x=1,5⇒x=12
⇒0,5−y+2y=2⇒2,5−yy=2⇒2,5−y=2y⇒3y=2,5⇒y=56⇒0,5−y+2y=2⇒2,5−yy=2⇒2,5−y=2y⇒3y=2,5⇒y=56
⇒z=0,5−12−56=−56⇒z=0,5−12−56=−56
Vậy x=12,y=56,z=−56
a) n−n = 0
b) n:n(n≠0) = 1
c) n+0 = n
d) n−0 = n
e) n.0 = 0
g) n.1= n
h) n:1=n
\(a,2019-7\left(x+1\right)=100\)
=>\(7\left(x+1\right)=2019-100=1919\)
( đến đoạn này có 2 cách làm , bạn thích chọn cách nào thì làm nha ! )
=>\(\left[{}\begin{matrix}x+1=1919:7\\7x+7=1919\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x+1=\frac{1919}{7}\\7x=1919-7=1912\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\frac{1919}{7}-1=\frac{1912}{7}\\x=\frac{1912}{7}\end{matrix}\right.\)
Vậy x ∈ {\(\frac{1912}{7}\)}
\(b,\left(3x-6\right).3=34\)
=>\(3x-6=\frac{34}{3}\)
=>\(3x=\frac{34}{3}+6=\frac{52}{3}\)
=> \(x=\frac{52}{3}:3=\frac{52}{9}\)
Vậy x ∈ {\(\frac{52}{9}\)}
a) |x+y||x+y| \(\le\)≤ |x|+|y|
Bình 2 vế của bđt
(|x+y|2)\(\le\)(|x|+|y|)2
\(\Leftrightarrow x^2+y^2+2xy\le x^2+y^2+2\left|xy\right|\)
\(\Leftrightarrow xy\le\left|xy\right|\) luôn đúng
Dấu = khi \(xy\ge0\)
-->Đpcm
b: \(\Leftrightarrow n-2+5⋮n-2\)
\(\Leftrightarrow n-2\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{3;1;7;-3\right\}\)
c: \(\Leftrightarrow n-3+4⋮n-3\)
\(\Leftrightarrow n-3\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{4;2;5;1;7;-1\right\}\)
d: \(\Leftrightarrow n-5+4⋮n-5\)
\(\Leftrightarrow n-5\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{6;4;7;3;9;1\right\}\)
e: \(\Leftrightarrow3n-3+4⋮n-1\)
\(\Leftrightarrow n-1\in\left\{1;-1;2;-2;4;-4\right\}\)
hay \(n\in\left\{2;0;3;-1;5;-3\right\}\)
Ta thấy: \(\left\{\begin{matrix}\left|x+5\right|\ge0\\\left|y-3\right|\ge0\end{matrix}\right.\)
\(\Rightarrow\left|x+5\right|+\left|y-3\right|\ge0\)
Mà \(\left|x+5\right|+\left|y-3\right|=0\) suy ra
\(\left\{\begin{matrix}\left|x+5\right|=0\\\left|y-3\right|=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x+5=0\\y-3=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=-5\\y=3\end{matrix}\right.\)
\(\left|x+5\right|\left|x+5\right|+\left|y-3\right|\left|y-3\right|=0\)
<=>\(\left|x+5\right|^2+\left|y-3\right|^2=0\)
<=>\(\left(x+5\right)^2+\left(y-3\right)^2=0\left(1\right)\)
Vì \(\left(x+5\right)^2\ge0\text{ với mọi x },\left(y-3\right)^2\ge0\text{ với mọi y}\)
Nên \(\left(1\right)\)<=>\(\left\{\begin{matrix}\left(x+5\right)^2=0\\\left(y-3\right)^2=0\end{matrix}\right.\)
<=>\(\left\{\begin{matrix}x+5=0\\y-3=0\end{matrix}\right.\)
<=>\(\left\{\begin{matrix}x=-5\\y=3\end{matrix}\right.\)
Vậy x=-5, y=3.