Найдите наибольшее целое решение неравенства
[tex]|4x-x^2-6|+|x+5|\leq x^2-5x+1[/tex]
-x^2+4x-6=-(x^2-4x+6)=-((x-2)^2+2)<0
(x^2-4x+6)+|x+5|<=x^2-5x+1
-4x+6+5x-1+|x+5|<=0
x+5+|x+5|<=0
x+5=t
t>=0
2t<=0 t<=0 t=0 x=-5
t<0
0<=0 x<=-5
x=-5
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Verified answer
-x^2+4x-6=-(x^2-4x+6)=-((x-2)^2+2)<0
(x^2-4x+6)+|x+5|<=x^2-5x+1
-4x+6+5x-1+|x+5|<=0
x+5+|x+5|<=0
x+5=t
t>=0
2t<=0 t<=0 t=0 x=-5
t<0
0<=0 x<=-5
x=-5