Question

Cho: P+Q= 2x²+5x²-3xy

: P-Q= x²-y²+2xy

Tìm:P,Q

Answer 1

Ta có : (P+Q)+(P-Q)\(=2x^2+5x^2-3xy+x^2-y^2+2xy\)

\(\Leftrightarrow2P=8x^2-xy-y^2\\ \Leftrightarrow P=4x^2-\dfrac{1}{2}xy-\dfrac{1}{2}y^2\)

\(\Rightarrow Q=\left(P+Q\right)-P=2x^2+5x^2-3xy-\left(4x^2-\dfrac{1}{2}xy-\dfrac{1}{2}y^2\right)\)

\(=2x^2+5x^2-3xy-4x^2+\dfrac{1}{2}xy+\dfrac{1}{2}y^2\\ =3x^2-\dfrac{5}{2}xy+\dfrac{7}{2}y^2\)