Tìm đa thức P(x) và Q(x) biết: P(x)+Q(x)=x^2+1;P(x)-Q(x)=2x 06/11/2021 Bởi Mackenzie Tìm đa thức P(x) và Q(x) biết: P(x)+Q(x)=x^2+1;P(x)-Q(x)=2x
$P(x)+Q(x)=x^2+1;P(x)-Q(x)=2x$ $ ⇒ P(x) + Q(x) + P(x) – Q(x) = x²+1+2x $ $⇔ 2P(x)=x²+1+2x$ $⇔P(x)=\frac{1}{2} x^2+ \frac{1}{2} +x$ $⇒Q(x)=x²+1-\frac{1}{2} x^2 – \frac{1}{2} -x$ $⇔O(x)= \frac{1}{2}x^2+\frac{1}{2} – x$ Bình luận
$P(x)+Q(x)+[P(x)-Q(x)]$ $=2.P(x) = x^2+2x+1$ $\to P(x) = \dfrac{x^2+2x+1}{2}$ $P(x)+Q(x)-[P(x)-Q(x)]$ $=2.O(x) = x^2-2x+1$ $\to Q(x) = \dfrac{x^2-2x+1}{2}$ Bình luận
$P(x)+Q(x)=x^2+1;P(x)-Q(x)=2x$
$ ⇒ P(x) + Q(x) + P(x) – Q(x) = x²+1+2x $
$⇔ 2P(x)=x²+1+2x$
$⇔P(x)=\frac{1}{2} x^2+ \frac{1}{2} +x$
$⇒Q(x)=x²+1-\frac{1}{2} x^2 – \frac{1}{2} -x$
$⇔O(x)= \frac{1}{2}x^2+\frac{1}{2} – x$
$P(x)+Q(x)+[P(x)-Q(x)]$
$=2.P(x) = x^2+2x+1$
$\to P(x) = \dfrac{x^2+2x+1}{2}$
$P(x)+Q(x)-[P(x)-Q(x)]$
$=2.O(x) = x^2-2x+1$
$\to Q(x) = \dfrac{x^2-2x+1}{2}$