已知x 加y=3,a加b=5,xy=1,ab=3,且 m=ax加by,n=bx加ay,求m的平方乘以n的平方
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![已知x 加y=3,a加b=5,xy=1,ab=3,且 m=ax加by,n=bx加ay,求m的平方乘以n的平方](/uploads/image/z/3173995-19-5.jpg?t=%E5%B7%B2%E7%9F%A5x+%E5%8A%A0y%3D3%2Ca%E5%8A%A0b%3D5%2Cxy%3D1%2Cab%3D3%2C%E4%B8%94+m%3Dax%E5%8A%A0by%2Cn%3Dbx%E5%8A%A0ay%2C%E6%B1%82m%E7%9A%84%E5%B9%B3%E6%96%B9%E4%B9%98%E4%BB%A5n%E7%9A%84%E5%B9%B3%E6%96%B9)
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已知x 加y=3,a加b=5,xy=1,ab=3,且 m=ax加by,n=bx加ay,求m的平方乘以n的平方
已知x 加y=3,a加b=5,xy=1,ab=3,且 m=ax加by,n=bx加ay,求m的平方乘以n的平方
已知x 加y=3,a加b=5,xy=1,ab=3,且 m=ax加by,n=bx加ay,求m的平方乘以n的平方
x+y=3,a+b=5,xy=1,ab=3,m=ax+by,n=bx+ay
m²+n²=(ax+by)²+(bx+ay)²=x²(a²+b²)+y²(a²+b²)+4xyab
=(x²+y²)(a²+b²)+4*(xy)(ab)
=[(x+y)²-2xy][(a+b)²-2ab]+4*1*3
=(9-2)(25-2*3)+12
=7*19+12
=145
答:为145
m²+n²=(ax+by)²+(bx+ay)²=x²(a²+b²)+y²(a²+b²)+4xyab
=(x²+y²)(a²+b²)+4*(xy)(ab)
=[(x+y)²-2xy][(a+b)²-2ab]+4*1*3
=(9-2)(25-2*3)+12
=7*19+12
=145