Tìm tất cả các tam giác vuông có số đo các cạnh là các số nguyên dương và số đo diện tích bằng số đo chu vi.

       

   Gäi c¸c c¹nh cña tam gi¸c vu«ng lµ x , y , z ; trong ®ã c¹nh huyÒn lµ z

    (x, y, z lµ c¸c sè nguyªn dư­¬ng )

   Ta cã xy = 2(x+y+z) (1) vµ  x2 + y2 = z2 (2)                                                               

   Tõ (2) suy ra   z2 = (x+y)2 -2xy , thay (1) vµo ta cã :

                           z2 = (x+y)2 - 4(x+y+z)

                                z2 +4z =(x+y)2 - 4(x+y)

                                z2 +4z +4=(x+y)2 - 4(x+y)+4

                                (z+2)2=(x+y-2)2 , suy ra  z+2 = x+y-2                  

                                z=x+y-4  ; thay vµo (1)  ta ®ự­îc :

                                xy=2(x+y+x+y-4)

                                xy-4x-4y=-8

                                (x-4)(y-4)=8=1.8=2.4            

  Tõ ®ã ta t×m ®­îc c¸c gi¸ trÞ cña x , y , z lµ :

                   (x=5,y=12,z=13) ; (x=12,y=5,z=13) ;

                   (x=6,y=8,z=10) ; (x=8,y=6,z=10)                     

sao mà chữ nhỏ thế ? –  Hàn Thiên Dii 27-04-16 02:49 PM

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