Question

va rog...exercitiul 6...dau coroana....cat mai repede

Answer 1

   
[tex]\displaystyle \\ a=2^{1990} - 2^{1989} -2^{1988} = \\ =2^{1988+2} - 2^{1988+1} -2^{1988} = \\ =2^{1988} \cdot 2^2 -2^{1988}\cdot 2^1 -2^{1988} = \\ =2^{1988}(2^2-2^1-1) =2^{1988}(4-2-1) = \boxed{2^{1988}} \\ \\ \\ \frac{a}{x} = \frac{4^{9993}}{25} \\ \\ x\cdot 4^{9993} = 25a \\ \\ x= \frac{25a}{4^{9993} } =\frac{25\cdot 2^{1988}}{4^{9993} } = \\ \\ =\frac{25\cdot 2^{1988}}{\Big(2^2\Big)^{9993} } =\frac{25\cdot 2^{1988}}{2^{2\cdot 9993} } = [/tex]


[tex]\displaystyle \\ =\frac{25\cdot 2^{1988}}{2^{19986} } =25\cdot 2^{1988-19986}=25 \cdot 2^{-17998}= \frac{25}{2^{17998}} \\ \\ \\ R: ~~~\boxed{x= \frac{25}{2^{17998}} }[/tex]