xy≠1,5x2+2009x+9=0,9y2+2009y+5=0,则x÷y=()xy≠1,5x2+2009x+9=0,9y2+2009y+5=0,则x÷y=()

Question

x y ≠ 1 ,5 x2 + 2009x +9 =0 ,9y2 + 2009 y + 5 = 0 ,则 x ÷ y = ( )
x y ≠ 1 ,5 x2 + 2009x +9 =0 ,9y2 + 2009 y + 5 = 0 ,则 x ÷ y = ( )

Answer 1

5x^2 + 2009x + 9 = 0 1)
9y^2 + 2009y + 5 = 0 2)
1)×5-2）×9,得
5(5x^2+2009x)-9(9y^2+2009y)=0
25x^2-81y^2+2009(5x-9y)=0
(5x-9y)(5x+9y+2009)=0
所以5x-9y=0或5x+9y+2009=0
当5x+9y+2009=0时,由1）,得
x(5x+2009)+9=0
x(-9y)+9=0
xy=1
与题设不符,
所以只有5x-9y=0成立
即x÷y=9/5