已知X^2-4X+Y^2-10Y+29=0,求X^2Y^2+2X^3Y^2+X^4Y^2
问题描述:
已知X^2-4X+Y^2-10Y+29=0,求X^2Y^2+2X^3Y^2+X^4Y^2
答
x^2-4x+y^2-10y+29
=(x^2-4x+4)+(y^2-10y+25)
=(x-2)^2+(y-5)^2
=0
所以x=2,y=5
因此 X^2Y^2+2X^3Y^2+X^4Y^2
=4*25+2*8*25+16*25
=900