Question

Dau 100 de puncte pentru exercitiile 30 si 31

Answer 1

[tex]E(x)=[(\frac{x+5}{x-5})^2+1+\frac{2x+10}{x-5}]\cdot \frac{x-5}{4x}+2\\ a)(x-5)^2=0 \Rightarrow x=5\\ x-5=0\Rightarrow x=5\\ 4x=0\Rightarrow x=0\\ S:x \in \{0,5\}\\ b)E(x)=(\frac{x^2+10x+25}{(x-5)^2}+1+\frac{2x+10}{x-5})\cdot \frac{x-5}{4x}+2\\ E(x)=\frac{x^2+10x+25+(x-5)^2+2(x+5)(x-5)}{(x-5)^2}\cdot \frac{x-5}{4x}+2\\ E(x)=\frac{x^2+10x+25+x^2-10x+25+2x^2-50}{(x-5)^2}\cdot \frac{x-5}{4x}+2\\ E(x)=\frac{4x^2}{x-5}\cdot \frac{1}{4x}+2\\ E(x)=\frac{x}{x-5}+2\\ E(x)=\frac{x+2x-10}{x-5}\\ [/tex]
[tex]E(x)=\frac{3x-10}{x-5}\\ c)E(a)=\frac{3a-10}{a-5} \in Z\\ a-5/a-5\Rightarrow a-5/3a-15\\ a-5/3a-10\Rightarrow a-5/3a-10\\ Le\ scadem:\ a-5/-5 \Rightarrow a-5 \in D5\\ a-5 \in \{-1,1,-5,5\}\\ a \in \{4,6,0,10\}\\ Dar\ a \notin \{0,5\} \Rightarrow S:a \in \{4,6,10\}\\ d)E(x)=4\\ \frac{3x-10}{x-5}=4\\ 3x-10=4x-20\\ 3x-4x=-20+10\\ -x=-10 \Rightarrow x=10[/tex]