Réponse :
Bonjour,
Explications étape par étape
Comme 48=2^4*3, il y a donc 5*2=10 possibilités
div 48={1,48,2,24,3,16,4,12,6,8}
[tex]x^2-y^2=48 \ \Longrightarrow\ (x+y)(x-y)=48\\Comme\ x+y > x-y\\\\1)\\\left \{ \begin {array} {ccc}x+y&=&48\\x-y&=&1\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}2x&=&49\ impossible \\x-y &=&1\\\end {array} \right.\\\\[/tex]
[tex]2)\\\left \{ \begin {array} {ccc}x+y&=&24\\x-y&=&2\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}x&=&13 \\y &=&11\\\end {array} \right.\\\\[/tex]
[tex]3)\\\left \{ \begin {array} {ccc}x+y&=&16\\x-y&=&3\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}2x&=&17\ impossible \\x-y &=&1\\\end {array} \right.\\\\[/tex]
[tex]4)\\\left \{ \begin {array} {ccc}x+y&=&12\\x-y&=&4\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}x&=&8 \\y &=&4\\\end {array} \right.\\\\[/tex]
[tex]5)\\\left \{ \begin {array} {ccc}x+y&=&8\\x-y&=&6\\\end {array} \right.\\\\\\\left \{ \begin {array} {ccc}x&=&7 \\y &=&1\\\end {array} \right.\\\\[/tex]
Sol={(13,11),(8,4),(7,1)}