已知x,y满足x²+y²-4x-6y+13=0,求(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2的值
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![已知x,y满足x²+y²-4x-6y+13=0,求(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2的值](/uploads/image/z/2576725-61-5.jpg?t=%E5%B7%B2%E7%9F%A5x%2Cy%E6%BB%A1%E8%B6%B3x%26%23178%3B%2By%26%23178%3B-4x-6y%2B13%3D0%2C%E6%B1%82%EF%BC%88-+y%2Fx%5E3%29%5E3%C3%B7%28-+1%2Fxy%29%5E4.%28x%2Fy%5E2%29%5E2%E7%9A%84%E5%80%BC)
已知x,y满足x²+y²-4x-6y+13=0,求(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2的值
已知x,y满足x²+y²-4x-6y+13=0,求(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2的值
已知x,y满足x²+y²-4x-6y+13=0,求(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2的值
x²+y²-4x-6y+13=0
x²-4x+4+y²-6y+9=0
(x-2)²+(y-3)²=0
x=2 y=3
(- y/x^3)^3÷(- 1/xy)^4.(x/y^2)^2
=-y^3/x^9 * x^4y^4*x^2/y^4
=-y^3/x^3
=-(y/x)³
=-(3/2)³
=-27/8
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x²+y²-4x-6y+13=0
x²-4x+4+y²-6y+9=0
(x-2)²+(y-3)²=0
∵(x-2)²≥0 (y-3)²≥0
∴x=2 y=3
于是
(-y/x^3)^3÷(-1/xy)^4*(x/y^2)^2
= -y^3/x^9 *x^4y^4*x^2/y^4
= -y^3/x^3
= -3^3/2^3
= -27/8