решите уравнение 1/2 (x+2) + 1/3 (x+3) + 1/5 (x-5) = 2

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

1/2 (x+2) + 1/3 (x+3) + 1/5 (x-5) = 2

1/2 х+1+1/3 х+1+1/5 х-1=2

1/2 х+1/3 х+1/5 х=2+1-1-1

х=30/31