Question

Fie a=2^2012+2^2013 si b=4^1006+4^1007 determinati a/b

Va rog! Dau coroană!

Answer 1

$a = 2^{2012}+2^{2013}\\ b = 4^{1006}+4^{1007}= 2^{2\cdot 1006}+2^{2\cdot 1007}=2^{2012}+2^{2014}\\ \\ \\ \dfrac{a}{b} = \dfrac{2^{2012}+2^{2013}}{2^{2012}+2^{2014}} = \dfrac{2^{2012}\cdot(1+2)}{2^{2012}\cdot (1+2^2)} = \dfrac{1+2}{1+4}=\boxed{\dfrac{3}{5}}$

Answer 2

Răspuns:

a/b = 3/5

Explicație pas cu pas:

$a=2^{2012}+2^{2012+1}=2^{2012}+2*2^{2012}=2^{2012}*(1+2)=3*2^{2012}\\b=(2^{2})^{1006}+(2^{2})^{1007}=2^{2012}+2^{2014}=2^{2012}+2^{2012+2}=2^{2012}*(1+2^{2})=5*2^{2012}.\\\frac{a}{b}=\frac{3*2^{2012}}{5*2^{2012}}=\frac{3}{5}$