Question

Doar primul subiect va rog din toata inima ajutatimi am mare nevoie dau coroana

Answer 1

   
[tex]\displaystyle\\ \texttt{Subiectul I}\\\\ 1a)\\ \frac{1}{6}= 0,1(6) = 0,166...\\\\ \text{Suma primelor 3 zecimale este: }~1+6+6 = \boxed{13}\\\\ b)\\ \text{Opusul numarului:}\\ \frac{1}{ \sqrt{8} -1} -\frac{1}{ \sqrt{8} +1}~\text{este}~-\left( \frac{1}{ \sqrt{8} -1} -\frac{1}{ \sqrt{8} +1}\right)=\\\\ =- \frac{1}{ \sqrt{8} -1} +\frac{1}{ \sqrt{8} +1}=\\\\ =- \frac{\sqrt{8} +1}{ (\sqrt{8} -1)(\sqrt{8} +1)} +\frac{\sqrt{8} -1}{ (\sqrt{8} +1)(\sqrt{8} -1)}= [/tex]


[tex]\displaystyle\\ =\frac{-\sqrt{8} -1}{ 8 -1} +\frac{\sqrt{8} -1}{ 8 -1}=\\\\ =\frac{-\sqrt{8} -1+ \sqrt{8} -1}{ 7} = \boxed{-\frac{2}{7}} \\\\ c)~\text{este gresit.}\\\\\\ 2)\\ a)\\ |3x-1|=5\\ 3x-1 = \pm 5\\ 3x-1 = 5~~\Rightarrow~~3x=5+1~~\Rightarrow~~3x = 6 ~~\Rightarrow~~x_1 = \boxed{2}\\ 3x-1 = -5~~\Rightarrow~~3x=-5+1~~\Rightarrow~~3x = -4 ~~\Rightarrow~~ x_2 = \boxed{ -\frac{4}{3} } [/tex]


[tex]\displaystyle\\ b)\\ x^2-7x+15=3\\ x^2-7x+15-3=0\\ x^2-7x+12=0\\\\ x_{12}= \frac{7\pm \sqrt{49-48} }{2} =\frac{7\pm\sqrt{1} }{2}=\frac{7\pm1}{2}\\\\ x_1 = \frac{7+1}{2} = \frac{8}{2} = \boxed{4}\\\\ x_2 = \frac{7-1}{2} = \frac{6}{2} = \boxed{3}\\\\ c) 1+4+7+\cdots + x=145\\\\ \text{Calculam numarul de termeni:}\\\\ n = \frac{x-1}{3}+1 = \frac{x-1+3}{3}= \frac{x+2}{3}\\\\ \text{Calculam suma cu Gauss:}\\\\ S= \frac{\dfrac{x+2}{3}(x+1)}{2}= \frac{(x+2)(x+1)}{6}\\\\ [/tex]


[tex]\displaystyle\\ \text{Scriem ecuatia:}\\\\ \frac{(x+2)(x+1)}{6} =145\\\\ (x+2)(x+1)=145 \cdot 6 (x+2)(x+1)=870\\\\ (x+2)(x+1)=30 \cdot 29 \\\\ \Longrightarrow~~~x+2 = 30~~ \Longrightarrow~~x = 30 - 2 = \boxed{28} [/tex]