Question

va rog frumos dau coroana su 100 de puncte
Ex 5,6​

Answer 1

5.

$\it 0,08(3)=\dfrac{83-8}{900}=\dfrac{\ 75^{(75}}{900}=\dfrac{1}{12};\ \ \ 0,03=\dfrac{3}{100}\\ \\ \\ Ecua\c{\it t}ia\ \ devine:\\ \\ \\ -\dfrac{1}{12}x^2=-\dfrac{3}{100}\Big |_{\cdot(-1)} \Rightarrow \dfrac{1}{12}x^2=\dfrac{3}{100}\Big|_{\cdot12} \Rightarrow x^2=\dfrac{\ 36}{100} \Rightarrow\\ \\ \\ \Rightarrow x^2=0,36 \Rightarrow \sqrt{x^2}=\sqrt{0,36}\Rightarrow |x|=0,6\Rightarrow x=\pm0,6\Rightarrow \\ \\ x\in\{-0,6;\ 0,6\}$

6.

$\it (2x-5)^2=45 \Rightarrow \sqrt{(2x-\sqrt5)^2}=\sqrt{45} \Rightarrow |2x-\sqrt5|=3\sqrt5 \Rightarrow \\ \\ \\ \Rightarrow 2x-\sqrt5=\pm3\sqrt5 \Rightarrow \begin{cases} \it 2x-\sqrt5=-3\sqrt5|_{+\sqrt5} \Rightarrow 2x=-2\sqrt5|_{:2} \Rightarrow x_1=-\sqrt5\\ \\ \it 2x-\sqrt5=3\sqrt5|_{+\sqrt5} \ \Rightarrow \ 2x=4\sqrt5|_{:2}\ \Rightarrow \ x_2=2\sqrt5} \end{cases}$