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