若X+3Y=0,XY≠0 求X²-3XY/XY+Y²的值

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若X+3Y=0,XY≠0 求X²-3XY/XY+Y²的值
若X+3Y=0,XY≠0 求X²-3XY/XY+Y²的值

若X+3Y=0,XY≠0 求X²-3XY/XY+Y²的值
x+3y=0 => x=-3y => x/y=-3
原式= (x^2-3xy)/(xy+y^2) 上下各除个y^2
= [(x/y)^2-3(x/y)]/[(x/y)+1] 代入x/y=-3
= [(-3)^2-3(-3)]/[-3+1]
= -9