Задание:
|x^2-8x+15| <= |15-x^2|
Решение:
x^2-8x+15=0x1=5x2=315-x^2=0x=sqrt (15) x=-sqrt (15) 1) x>=5 x^2-8x+15 <= -15+x^2 -8x <= -30 x>=15/4 x>=52) ]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[
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