Question

Tìm x,y nguyên : 

x² + y² + 5x²y² + 60 = 37xy

Answer 1

Trả lời

5.494−54(2xy−7)2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline; float:none; line-height:normal; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax">5.494−54(2xy−7)2

⇔[2(x−y)]2+5(2xy−7)2=5.49−60.4=5⇔[2(x−y)]2+5(2xy−7)2=5.49−60.4=5

x;y∈Z;2xy−7≠0;5(2xy−7)2≥5⇒[2(x−y)]2=0→x=yx;y∈Z;2xy−7≠0;5(2xy−7)2≥5⇒[2(x−y)]2=0→x=y

|(2xy−7)|=1|(2xy−7)|=1 [2x2−7=−1;x2=3(l)2x2−7=1;x2=4(n)[2x2−7=−1;x2=3(l)2x2−7=1;x2=4(n)⇔(x;y)=(±2;±2)