Question

x=2 la puterea 1998+2 la putera1999+2 la puterea 2000
y=2la purterea 2003 -2la puterea 2002-2 la puterea2001-2 la putera2000
 Comparati termenii
Va rog sa ma ajutati

Answer 1

$x=2^{1998}+2^{1999}+2^{2000} \\\\ x=2^{1998}(1+2+2^2) \\\\ x=2^{1998}(3+4) \\\\ \boxed{x=2^{1998}*7} \\\\\\y=2^{2003}-2^{2002}-2^{2001}-2^{2000} \\\\ y= 2^{2000}(2^3-2^2-2-1)\\\\ y=2^{2000}(8-4-3) \\\\ y=2^{2000}*1 \\\\ \boxed{y=2^{2000}} \\\\\\ x \ de \ comparat \ y \\\\ 2^{1998}*7 \ de \ comparat \ 2^{2000} \\\\ 2^{1998}*7 \ de \ comparat \ 2^{1998}*2^2 \\\\ 2^{1998}*7 > 2^{1998}*4 \\\\ \boxed{\boxed{x>y}}$