Question

ajutați-mă vă roog!!!!​

Answer 1

 

$\displaystyle\bf\\3)\\a)\\\\(-8+10-12+14-\hdots-296+298):(-4+5-6+7-\hdots-148+149)\\\\\text{Facem abstractie de semne pentru a calcula numarul de termeni}\\\text{in fiecare din cele 2 paranteze.}\\\\\^In~prima~parantez\u a\!:\\\\n_1=\frac{298-8}{2}+1=\frac{290}{2}+1=145+1=146~termeni\\\\\^In~a~doua~parantez\u a\!:\\\\n_2=149-4+1=145+1=146~termeni\\\\146=numar~par\\\\In~fiecare~paranteza~grupam~termenii~cate~2.\\Rezulta~~146:2=73~de~grupe~in~fiecare~paranteza.$

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$\displaystyle\bf\\~\Big[\underbrace{(-8+10)}_{=2}+\underbrace{(-12+14)}_{=2}+(-\hdots+\underbrace{(-296+298)}_{=2}\Big]:\\\\:\Big[\underbrace{(-4+5)}_{=1}+\underbrace{(-6+7)}_{=1}+(-\hdots+\underbrace{(-148+149)}_{=1}\Big]=\\\\=\Big[\underbrace{2+2+\hdots+2}_{73~de~2-uri}\Big]: \Big[\underbrace{1+1+\hdots+1}_{73~de~1-uri}\Big]=\\\\=\Big[73\times2\Big]:\Big[73\times1\Big]146:73=\boxed{\bf2}\\\\\\b)\\\\Vezi~paranteza~1~de~la~a)\\\\(-8+10-12+14-\hdots-296+298):(-146)=146:(-146)=\boxed{(\bf-1)}$

Answer 2

a) Înlocuim împărțirea cu o linie de fracție și obținem:

$\dfrac{-8+10-12+14- ...-296+298}{-4+5-6+7-...-146+149}=\dfrac{2(-4+5-6+7-... -146+149)}{-4+5-6+7-...-146+149}=2$