Question

Compară numerele a=2017²-3² și b=2018²-4²​

Answer 1

 

$\displaystyle\bf\\a=2017^2-3^2=2017^2-9\\\\b=2018^2-4^2=\\=(2017+1)^2-16=\\=2017^2+2\times2017+1-16=\\=2017^2+4034+1-16=\\=2017^2+4033-16=\\=2017^2+4017\\\\4017> (-9)\\\\\implies 2017^2-9<2017^2+4017\\\\\implies 2017^2-3^2 < 2018^2-4^2\\\\\implies a<b$