Question

subpunctul c va rog​

Answer 1

(x-1)²⁰¹⁷+(x-2)²⁰¹⁷=0

(x-1)²⁰¹⁷=-(x-2)²⁰¹⁷

Avand in vedere ca exponentul este impar, putem scrie si asa

-(x-2)²⁰¹⁷=(-x+2)²⁰¹⁷=(2-x)²⁰¹⁷

(x-1)²⁰¹⁷=(2-x)²⁰¹⁷ => x-1=2-x => x=3/2

Dar, dupa cum se vede avem 2017 radacini, deci fiecare dintre cele 2017 radacini este 3/2.

Suma x₁+x₂+.....+x₂₀₁₇=3*2017/2=6051/2

Answer 2

$f = (X-1)^{2017}+(X-2)^{2017} \\ \\ f=a_{2017}X^{2017}+a_{2016}X^{2016}+...+a_1X+a_0 \\ \\ S = -\dfrac{a_{2016}}{a_{2017}} \\ \\ \\ f = C_{2017}^0 X^{2017}+C_{2017}^{1}X^{2016}\cdot (-1)^{1}+C_{2017}^2X^{2015}\cdot (-1)^{2}+... \\ \\+C_{2017}^0X^{2017}+C_{2017}^1X^{2016}\cdot (-2)^1 +C_{2017}^{1}X^{2015}\cdot (-2)^2+...\\ \\ \\\Rightarrow a_{2016} = -C_{2017}^1+\Big(-2C_{2017}^1) = -2017-2\cdot 2017 = -6051\\ \Rightarrow a_{2017} =C_{2017}^0+C_{2017}^0 = 1+1 = 2$

$\Rightarrow S = -\dfrac{-6051}{2}= \Rightarrow \boxed{S = \dfrac{6051}{2}}$