已知x、y满足x2+y2+174=4x+y，求代数式xyx+y的值．

Question

已知x、y满足x²+y²+(17)/(4)=4x+y，求代数式(xy)/(x+y)的值．

Answer 1

将x²+y²+(17)/(4)=4x+y，变形得：（x²-4x+4）+（y²-y+(1)/(4)）=0，
即（x-2）²+（y-(1)/(2)）²=0，
解得：x=2，y=(1)/(2)，
则原式=(2×(1)/(2))/(2+(1)/(2))=(2)/(5)．