Question

已知A=x²+xy+y²,B=x²-xy+y²……

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)的值
希望可以列出算式来解答
谢谢大家了~

Answer 1

解
x²+3xy+4y²=2
4x²-2xy+y²=3
两式相加得：
5x²+xy+5y²=5

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

Answer 2

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