Question

help me.

Answer 1

Lời giải:
Xét hiệu:

$(5^{200}+3)(5^{202}+1)-(5^{201}+3)(5^{201}+1)$

$=5^{402}+5^{200}+3.5^{202}+3-(5^{402}+4.5^{201}+3)$

$=5^{200}+3.5^{202}-4.5^{201}$

$=5^{200}(1-5)+3.5^{201}(5-1)$

$=-4.5^{200}+4.3.5^{201}=4.5^{200}(15-1)=14.4.5^{200}>0$

$\Rightarrow (5^{200}+3)(5^{202}+1)> (5^{201}+3)(5^{201}+1)$

$\Rightarrow M> N$