Question

已知A=x²+xy+y².,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3。

已知A=x²+xy+y².,B=x²-xy+y²,x²+3xy+4y²=2,4x²-2xy+y²=3。求代数式4A+B-(A-B)

Answer 1

A=x²+xy+y²,.,B=x²-xy+y²
3A=3x²+3xy+3y²
2B=2x²-2xy+2y²

x²+3xy+4y²=2,...(1)
4x²-2xy+y²=3...(2)
(1)+(2)得
5x²+xy+5y²=5

4A+B-(A-B)＝3A+2B=3x²+3xy+3y²+2x²-2xy+2y²
=5x²+xy+5y²
=5

Answer 2

原式=4A+B-A+B
=3A+2B
=3x²+3xy+3y²+2x²-2xy+2y²
=5x²+xy+5y²
=(x²+3xy+4y²)+(4x²-2xy+y²)
=2+3
=5