Question

|x^2-8x+15| <= |15-x^2|

Answer 1

x^2-8x+15=0

x1=5

x2=3

15-x^2=0

x=sqrt(15)

x=-sqrt(15)

1) x>=5  x^2-8x+15<=-15+x^2   -8x<=-30  x>=15/4   x>=5

2) ]sqrt(15);5[ -x^2+8x-15<=x^2-15           2x^2-8x>=0  2x(x-4)>=0   [4;5]

3) ]3;sqrt(15)] -x^2+8x-15<=15-x^2   8x<=30  x<=15/4  ]3;15/4]

4) ]-sqrt(15);3] x^2-8x+15<=15-x^2   2x(x-4)<=0   [0;4]   [0;3]

5) x<-sqrt(15) x^2-8x+15<=x^2-15   8x>=30  x>=15/4

 

[0;15/4] U [4;бесконечность[