Question

factorul ccomun si puteriile!!
calculeaza :
a)44 la puterea 10 -3 ori 4 la put. 9 ^-3 sus ori 4 ^8 ^- 3 sus ori 4 ^7-.....-3
b)2^10 ori a - 2 ^9 ori b daca 2 ori a -b =17
c)2 ^15-2^14-2^13-2^12 ori.....-2-1
atentie 2^9 ori 2 = 22^a^+1

Answer 1

[tex]a)4\cdot 4^{10}-3\cdot 4^{9}-3\cdot 4^{8}-_{\dots}-3=\\ 7\cdot 4^{10}-3\cdot 4^{10}-3\cdot 4^{9}-3\cdot 4^{8}-_{\dots}-3=\\ 7\cdot 4^{10}-3\cdot (4^{10}+4^{9}+ 4^{8}+_{\dots}+1)=\\ Notam:\\ S=1+4+4^2+_{\dots}+4^{10}|\cdot 4\\ 4S=4+4^2+_{\dots}+4^{11}\\ -------------\\ 4S-S=4^{11}-1\\ S=\dfrac{4^{11}-1}{3}\\ Revenind:\\ 7\cdot 4^{10}-\not 3\cdot \dfrac{4^{11}-1}{\not3}=4^{10}(7-4)+1=3\cdot 4^{10}+1 [/tex]
[tex]b)2\cdot a-b=17\\ 2^{10}\cdot a-2^{9}\cdot b=2^9(2\cdot a-b)=2^9\cdot 17\\ c)\text{Facem exact ca la a):}\\ S=1+2+2^2+_{\dots}+2^{14}\\ 2S=2+2^2+2^3+_{\dots}+2^{15}\\ ------------\\ 2S-S=2^{15}-1\Rightarrow S=2^{15}-1\\ Revenind: 2^{15}-2^{15}+1=\boxed{1}[/tex]