Question

determine os valores de a, b e c sabendo que x2-2x+1=a(x2+x+1)+(bx+c).(x+1)

Answer 1

Resposta:

a = 4

b = -3

c = -3

Explicação passo-a-passo:

$x^{2}-2x+1=a(x^{2} +x+1)+(bx+c)(x+1)\\x^{2} -2x+1=ax^{2} +ax+a+bx^{2} +bx+cx+c\\x^{2} -2x+1=ax^{2}+bx^{2} +ax+bx+cx+a+c \\x^{2} -2x+1=(a+b)x^{2} +(a+b+c)x+a+c$

Igualando os coeficientes:

$a+b = 1\\a+b+c = -2\\a+c = 1\\\\a+b = a+c\\b = c\\\\a+b+c = -2\\1 + c = -2\\c = -3\\\\Sendo:\\b = c\\b = -3\\\\a+c =1\\a-3=1\\a=4$