Question

Se A(x-3)(x-2)+Bx(x - 3) + Cx(x-2) = 12, calcule os valores de A, B e C.​

Answer 1

Resposta:

A=2, B= -6 e C=4

Explicação passo-a-passo:

A(x-3)(x-2)+Bx(x - 3) + Cx(x-2) = 12

A(x²-2x-3x+6)+Bx²-3Bx+Cx²-2Cx=12

Ax²-5Ax+6A +Bx²-3Bx+Cx²-2Cx=12

x²(A+B+C)+x(-5A-3B-2C)+6A=12

x²(0)+x(0)+6A=12

6A=12 => A=2

A+B+C=2+B+C=0 => B+C = -2 => C= -B-2

-5A-3B-2C=-5(2)-3B-2C=0 =>3B+2C= -10

B+C = -2 => B= -C-2 (1)

3B+2C= -10 =>3(-C-2)+2C= -3C-6+2C=-C-6= -10 => C=10-6=4

B=-4-2 = -6