15*(X+3)*(X-5) + 10*(X+2)*(X-5) +6*(X+2)*(X+3) \ 30*(X+2)*(X+3)*(X-5) = 2
15*(X^2-2X-15) +10*(X^2-3X-10) +6*(X^2+5X+6) = 60*(X+2)*(X+3)*(X-5)
15X^2 - 30X - 225 + 10X^2 - 30X - 100 +6X^2 +30X + 36 =
= 31X^2 - 30X - 289
60*(X+2)*(X+3)*(X-5) = 60*(X^2+5X+6)*(X-5) = 60*(X^3 - 19X -30) = 60X^3 - 1140X - 1800
31X^2 - 30X - 289 = 60X^3 - 1140X - 1800
60X^3 - 31X^2 - 1110X - 1511 = 0
Берём производную:
180X^2 - 62X - 1110X = 0
2*(90X^2 - 31X - 555) = 0
D = 961 - 4*90*(-555) = 961 + 199800=200761 V D = 448
X1 = 31 + 448 \ 180 = 2.6
X2 = 31 - 448 \ 180 = - 417\180 = - 2.3
15*(X+3)*(X-5) + 10*(X+2)*(X-5) +6*(X+2)*(X+3) \ 30*(X+2)*(X+3)*(X-5) = 2
15*(X^2-2X-15) +10*(X^2-3X-10) +6*(X^2+5X+6) = 60*(X+2)*(X+3)*(X-5)
15X^2 - 30X - 225 + 10X^2 - 30X - 100 +6X^2 +30X + 36 =
= 31X^2 - 30X - 289
60*(X+2)*(X+3)*(X-5) = 60*(X^2+5X+6)*(X-5) = 60*(X^3 - 19X -30) = 60X^3 - 1140X - 1800
31X^2 - 30X - 289 = 60X^3 - 1140X - 1800
60X^3 - 31X^2 - 1110X - 1511 = 0
Берём производную:
180X^2 - 62X - 1110X = 0
2*(90X^2 - 31X - 555) = 0
D = 961 - 4*90*(-555) = 961 + 199800=200761 V D = 448
X1 = 31 + 448 \ 180 = 2.6
X2 = 31 - 448 \ 180 = - 417\180 = - 2.3
y'=2-1/(x+3) x>-3
y'=0
1/(x+3)=2
1-2x-6=0
2x=-5
x=-2.5
y'(0)=2-1/3>0
y'(-2,6)=2-1/0,4<0
точка -2,5 точка минимума