讨论函数y=x^2-3|x|+7的图像与函数y=x^2-3x+|x^2-3x|+6的图像的交点个数.

y=x^2-3|x|+7
for x >0
y=x^2-3x+7
for xcase1中，x=(9-√85)/2不可以吗？y=x^2-3|x|+7
for x >0
y=x^2-3x+7

for x<=0
y=x^2+3x+7
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y=x^2-3x+|x^2-3x|+6
for 0y=x^2-3x-(x^2-3x)+6
= 6

for x>=3 or x<=0
y=x^2-3x+(x^2-3x)+6

= 2x^2 -6x+6
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case 1: x<=0
y=x^2+3x+7 (1)
y= 2x^2 -6x+6(2)
x^2+3x+7 = 2x^2 -6x+6
x^2-9x-1 =0
x = (9+√85) /2or(9-√85) /2
solution for case 1: (9-√85) /2

case 2: 0y=x^2-3x+7(1)
y=6 (2)
x^2-3x+7=6
x^2-3x+1=0
x= (3+√5)/2or(3-√5)/2
solution for case 2:x= (3+√5)/2or(3-√5)/2

case 3: x>=3
y=x^2-3x+7 (1)
y =2x^2 -6x+6 (2)
x^2-3x+7 =2x^2 -6x+6
x^2-3x-1 =0
x= (3+√13)/2 or(3-√13)/2
solution for case 3:(3+√13)/2

ie x= (3+√5)/2or(3-√5)/2 or (9-√85) /2 or (3+√13)/2