若z=3x(3y﹣x)﹣(4x﹣3y)(x+3y)
(1)若x,y均为整数,求证:当x是3的倍数时,z能被9整除;
(2)若y=x+1,求z的最小值.
解:(1)证明:
z=3x(3y﹣x)﹣(4x﹣3y)(x+3y)
=9xy﹣3x2﹣(4x2+9xy﹣9y2)
=9xy﹣3x2﹣4x2﹣9xy+9y2
=﹣7x2+9y2
∵x是3的倍数时,
∴z能被9整除.
(2)当y=x+1时,