[tex]1.2x+y=5\\
Deoarece\ 2x\ este\ par\ si\ 5\ este\ impar,inseamna\ ca\ y\ este\ impar.\\
Pentru\ y=3\Rightarrow x=1\\
(x,y)=(1,3)\\
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2. \left \{ {{2x-y=1} \atop {x+y=-4}} \right.\Leftrightarrow \left \{ {{2x-y=1} \atop {2x+2y=-8}} \right.\\
Prin\ scadere\ obtinem: /-3y=9\Rightarrow y=-3\\
2x+3=1\\
2x=-2\Rightarrow x=-1\\
S:(x,y)=(-1,-3)\\
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3. \left \{ {{3x-2\ \textless \ 7} \atop {4-2x\leq 3x+14}} \right. \\
Rezolvam\ fiecare\ inecuatie\ separat:\\
3x-2\ \textless \ 7\Rightarrow x\ \textless \ 3\Rightarrow S_1=(-\infty,3)\\
[/tex]
[tex]4-2x\leq 3x+14\\
-5x \leq 10\Rightarrow x\geq -2\Rightarrow S_2=[-2,\infty)\\
S=S_1\cup S_2=[-2,3)\\
Asadar:x\in \{-2,-1,0,1,2\}\\
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4.a)6x^2+0,5x=0\\
x(6x+0,5)=0\\
\Rightarrow x_1=0\\
\Rightarrow 6x+0,5=0\\
6x=-\frac{1}{2}\\
x_2=-\frac{1}{12}\\
S:x\in \{0,-\frac{1}{12}\}\\
b)3x^2+13x-10=0\\
\Delta=169+120=289\Rightarrow \sqrt{\Delta}=17\\
x_1=\frac{-13+17}{6}=\frac{2}{3}\\
x_2=\frac{-13-17}{6}=-5\\
S:x\in \{\frac{2}{3},-5\}\\
c)5x(5x+2)+3=2\\
25x^2+10x+1=0\\
(5x+1)^2=0\Rightarrow S:x=-\frac{1}{5}\\
[/tex]
[tex]5.Aplicam\ relatii\ lui\ Viet\acute{e}:\\
S=x_1+x_2=6\\
P=x_1\cdot x_2=(3-\sqrt2)(3+\sqrt2)=3-2=1\\
\boxed{x^2-Sx+P=0}\\
x^2-6x+1=0\\
\\
6.Not\breve{a}m: x=num\breve{a}rul\ b\hat{a}rnelor\ de\ stejar\\
~~~~~~~~~~~~~~~y=num\breve{a}rul\ b\hat{a}rnelor\ de\ brad\\
\left \{ {{x+y=300} \atop {46x=28y-1000}} \right. \Leftrightarrow \left \{ {{x+y=300} \atop {46x-28y=-1000}} \right. \Leftrightarrow \left \{ {{46x+46y=13800} \atop {46x-28y=-1000}} \right. \\
[/tex]
[tex]Dac\breve{a}\ sc\breve{a}dem\ relatiile\ obtinem:/74y=14800\Rightarrow y=200\\
x+200=300\Rightarrow x=100\\
R:100\ b\hat{a}rne\ de\ stejar\ si\ 200\ b\hat{a}rne\ de\ brad[/tex]
