Question

初二上册数学完全平方公式1.已知(x+y^2)=16,(x-y)^2=4,求x^2+xy+y^2

Answer 1

x^2+xy+y^2=13

因为(x+y^2)=x^2+2XY+Y^2=16 (x-y)^2=x^2-2XY+Y^2=4

x^2+2XY+Y^2-(x^2-2XY+Y^2)=4XY=12

XY=3

x^2+2XY+Y^2+(x^2-2XY+Y^2)=2x^2+2y^2=20

又∵2（x^2+y^2）=20,∴x^2+y^2=10

∴x^2+y^2+xy=13