Question

4x^2+7xy-2y^2是9的倍数,(1)x,y是整数(2)4x-y是3的倍数

Answer 1

4x^2+7xy-2y^2=(4x-y)(x+2y)=(4x-y)(x+2y+3x-3y-3x+3y)

=(4x-y)[(4x-y)-3(x-y)]

因此4x-y为3的倍数,所以(4x-y)-3(x-y)也为3的倍数

因此=(4x-y)[(4x-y)-3(x-y)]是9的倍数.