Đáp án:
$n$ $=$ $2001$
Giải thích các bước giải:
Gọi: $n$ $+$ $24$ $=$ $a^2$
$n$ $-$ $65$ $=$ $b^2$
Ta có: $a^2$ $+$ $b^2$ $=$ $n$ $+$ $24$ $+$ $n$ $-$ $65$ $($ Áp dụng HĐT $3$ $)$
$($$a$ $+$ $b$ $)$ $.$ $($ $a$ $-$ $b$ $)$ $=$ $89$
$($$a$ $+$ $b$ $)$ $.$ $($ $a$ $-$ $b$ $)$ $=$ $1$ $.$ $89$
Ta thấy: $a$ $-$ $b$ $<$ $a$ $+$ $b$
$⇒$ $a$ $-$ $b$ $=$ $1$ hay $a$ $+$ $b$ $=$ $89$
Suy ra:
$\left \{ {{a = (89+1):2} \atop b{= (89-1):2}} \right.$
$⇒$ $a$ $=$ $45$ , $b$ $=$ $44$
$\left \{ {{n+24=45^2}\atop{n -65 =44^2 }} \right.$
$\left \{ {{n+24=2025}\atop{n -65 =1936}} \right.$
$\left \{ {{n=2025-24}\atop{n=1936+65}} \right.$
$\left \{ {{n=2001}\atop{n=2001}} \right.$
$⇒$ $n$ $=$ $2001$
$#Dino.Team$
$@Shun$~$Aqua$~
