已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 22:55:29
已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值已知x+y=6,xy=7,求

已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值
已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值

已知x+y=6,xy=7,求(3x+y)*(3x+y)+(x+3y)*(x+3y)的值

x+y=6
两边平方
x²+2xy+y²=36
∵xy=7
∴x²+y²+2×7=36
∴x²+y²=22
(3x+y)*(3x+y)+(x+3y)*(x+3y)
=9x²+y²+x²+9y²
=10x²+10y²
=10(x²+y²)
=10×22
=220