Question

Va rog dau coroana!.va implor​

Answer 1

Răspuns:

4096

Explicație pas cu pas:

$a = \Big[2008 - \Big( \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + ... + \frac{1005}{1006}\Big) \Big] : \Big( \frac{4}{3} + \frac{5}{4} + \frac{6}{5} + ... + \frac{1007}{1006} \Big) = \\ = \Big[2008 - \Big(\underbrace{\frac{3 - 1}{3} + \frac{4 - 1}{4} + \frac{5 - 1}{5} + ... + \frac{1006 - 1}{1006}}_{1004 \: termeni}\Big) \Big] : \Big(\underbrace{\frac{3 + 1}{3} + \frac{4 + 1}{4} + \frac{5 + 1}{5} + ... + \frac{1006 + 1}{1006}}_{1004 \: termeni}\Big) \\ = \Big[2008 - \Big(1 - \frac{1}{3} + 1 - \frac{1}{4} + 1 - \frac{1}{5} + ... + 1 - \frac{1}{1006}\Big) \Big] : \Big(1 + \frac{1}{3} + 1 + \frac{1}{4} + 1 + \frac{1}{5} + ... + 1 + \frac{1}{1006} \Big) \\ = \Big[2008 - \Big(1 \cdot 1004 - \frac{1}{3} - \frac{1}{4} - \frac{1}{5} - ... - \frac{1}{1006}\Big) \Big] : \Big(1 \cdot 1004 + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{1006} \Big) \\ = \Big(2008 - 1004 + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{1006}\Big) : \Big(1004 + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{1006} \Big) \\ = \Big(1004 + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{1006}\Big) : \Big(1004 + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ... + \frac{1}{1006} \Big) = \red{ \bf 1}$

$a = 1$

${x}^{a} = 4096 \iff {x}^{1} = 4096 \implies \red{\bf x = 4096}$

(între 3 și 1006 sunt: 1006 - 3 + 1 = 1004 termeni)

Answer 2

$\it 200-\Big(\dfrac{2}{3}+\dfrac{3}{4}+\dfrac{4}{5}+\ ...\ +\dfrac{1005}{1006}\Big)=(\underbrace{ \it 2+2+2+\ ...\ +2}_{1004\ termeni})-\\ \\ \\ -\Big(\underbrace{ \it \dfrac{2}{3}+\dfrac{3}{4}+\dfrac{4}{5}+\ ...\ +\dfrac{1005}{1006}}_{1004\ termeni}\Big)=(2-\dfrac{2}{3})+(2-\dfrac{3}{4})+(2-\dfrac{4}{5})+\ ...\ +(2-\dfrac{1005}{1006})=\\ \\ \\ =\dfrac{4}{3}+\dfrac{5}{4}+\dfrac{6}{5}+\ ...\ +\dfrac{1007}{1006}$

$\it a=\Big(\dfrac{4}{3}+\dfrac{5}{4}+\dfrac{6}{5}+\ ...\ +\dfrac{1007}{1006}\Big):\Big(\dfrac{4}{3}+\dfrac{5}{4}+\dfrac{6}{5}+\ ...\ +\dfrac{1007}{1006}\Big)=1$

$\it x^a=4096 \Rightarrow x^1=4096 \Rightarrow x=4096$