初1数学因式分解已知2x-3y+
(1)。 2x2+3xy-9y2+z2+3xz = (2x-3y+z)(x+3y+z) = (0)(x+3y+z) = 0
(2)。 (x+y+z)(x2 +y2 +z2) = (x3+y3+z3) + (xy2+x2y+yz2+y2z+zx2+z2x) = 3*29
==> xy2+x2y+yz2+y2z+zx2+z2x = 3*29 - 45 = 42
(x+y+z)^3 = (x3+y3+z3) + 3*(xy2+x2y+yz2+y2z+zx2+z2x) + 6xyz = 3^3
==> xyz = (3^3 - 45 - 3*42)/6 = -24
(3)。 x、y为整数，3x...全部
(1)。 2x2+3xy-9y2+z2+3xz = (2x-3y+z)(x+3y+z) = (0)(x+3y+z) = 0
(2)。 (x+y+z)(x2 +y2 +z2) = (x3+y3+z3) + (xy2+x2y+yz2+y2z+zx2+z2x) = 3*29
==> xy2+x2y+yz2+y2z+zx2+z2x = 3*29 - 45 = 42
(x+y+z)^3 = (x3+y3+z3) + 3*(xy2+x2y+yz2+y2z+zx2+z2x) + 6xyz = 3^3
==> xyz = (3^3 - 45 - 3*42)/6 = -24
(3)。
x、y为整数，3x-y = 5k，可以推导出：x = 2y + 5m（m为整数）
因此：6x2+xy-y2 = 25*(y^2 + 5my + 6*m^2), 是25的倍数。
证毕。收起
