Question

P(x) + Q(x) = 6x² - 3x + 2

Q(x) + R(x) = -3x² + 7x - 5

R(x) + P(x) = -x² - 4x + 3

Tìm P(x) ; Q(x) ; R(x)

Answer 1

Cộng 3 đẳng thức vế với vế ta có:

\(2\left(P\left(x\right)+Q\left(x\right)+R\left(x\right)\right)=6x^2-3x+2-3x^2+7x-5-x^2-4x+3\)

=>\(2\left(P\left(x\right)+Q\left(x\right)+R\left(x\right)\right)=2x^2\)

=> \(P\left(x\right)+Q\left(x\right)+R\left(x\right)=x^2\)

=>\(\hept{\begin{cases}R\left(x\right)=x^2-\left(6x^2-3x+2\right)=-5x^2+3x-2\\P\left(x\right)=x^2-\left(-3x^2+7x-5\right)=4x^2-7x+5\\Q\left(x\right)=x^2-\left(-x^2-4x+3\right)=2x^2+4x-3\end{cases}}\)