已知x,y满足x²+y²-4x-6y+13=0,求(-y/x³)³÷(-1/xy)四次方×(x/y²)²

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已知x,y满足x²+y²-4x-6y+13=0,求(-y/x³)³÷(-1/xy)四次方×(x/y²)²
已知x,y满足x²+y²-4x-6y+13=0,求(-y/x³)³÷(-1/xy)四次方×(x/y²)²

已知x,y满足x²+y²-4x-6y+13=0,求(-y/x³)³÷(-1/xy)四次方×(x/y²)²
∵x2+y2-4x-6y+13=0
∴(x2-4x+4)+y^2-6y+9=0
(x-2)^ 2+(y-3) ^2=0
(x-2)^ 2≥0,(y-3)^ 2≥0.
x-2=0且y-3=0
x=2,y=3
∴(-y/x^3)^3÷(-1/xy)四次方×(x/y^2)^2
=(-3/8)^3÷(1/6)^4×(2/9)^2
=-27/512÷1/1296×4/81
=-3.375

(x²-4x+4)+(y²-6y+9)=0
(X-2)(X-2)+(Y-3)(Y-3)=0
x=2,y=3

x2+y2-4x-6y+13
=(x-2)^2+(y-3)^2
=0
所以 x-2=0 且 y-3=0
即 x=2 y=3
(-y/x3)3÷(-1/xy)四次方×(x/y2)2
=-y^3/x^9×(x^4y^4)×(x^2/y^4)
=-y^3/x^3
=-27/8