Question

已知x²+y²-2x-4y+5=0

已知x²+y²-2x+4y+5=0,求（x四次方-y四次方）/（x²-2xy+y²）·（x-y）/
（xy+y²）÷【（x²+y²）/y】²的值

Answer 1

已知x²+y²-2x+4y+5=0
x²-2x+1+y²+4y+4=0
(x-1)²+(y+2)²=0;
x-1=0;
x=1;
y+2=0;
y=-2;
（x四次方-y四次方）/（x²-2xy+y²）·（x-y）/（xy+y²）÷【（x²+y²）/y】²
=（x-y）(x+y)(x²+y²)/(x-y)²×(x-y)/y(x+y)×y²/(x²+y²)²
=y/(x²+y²)
=-2/(1+4)
=-2/5;