Răspuns:
a + b + c = - 6
Explicație pas cu pas:
(x - 2)³- 9x + 18 = (x + a)(x + b)(x + c)
(x - 2)³- 9x + 18 = (x - 2)³ - 9(x - 2) =
(x - 2) • [(x - 2)² - 9] = (x - 2) • [(x - 2)² - 3²] =
(x - 2) • (x - 2 - 3) • (x - 2 + 3) =
(x - 2) • (x - 5) • (x + 1) = (x + a) • (x + b) • (x + c)
⇒ a = - 2
⇒ b = - 5
⇒ c = 1
a + b + c = - 2 + (-5) + 1
a + b + c = - 2 - 5 + 1
a + b + c = - 6
==pav38==
[tex]\it (x-2)^3-9x+18= (x-2)^3-9(x-2)=(x-2)\[[(x-2)^2-3^2]=\\ \\ =(x-2)(x-2-3)(x-2+3)=(x-2)(x-5)(x+1)=(x+1)(x-2)(x-5)\\ \\ \\ Egalitatea\ \ din\ \ enun\c{\it t}\ \ devine:\\ \\ (x+1)(x-2)(x-5)=(x+a)(x+b)(x+c) \Rightarrow a=1,\ \ b=-2,\ \ c=-5.[/tex]
[tex]\it a+b+c=1-2-5=-6[/tex]