13x^2-6xy+y^2-4x+1=0,求(x+y)^13*x^10的值

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13x^2-6xy+y^2-4x+1=0,求(x+y)^13*x^10的值
13x^2-6xy+y^2-4x+1=0,求(x+y)^13*x^10的值

13x^2-6xy+y^2-4x+1=0,求(x+y)^13*x^10的值
亲,原式变形为
9x^2-6xy+y^2+4x^2-4x+1=0
(3x-y)^2+(2x-1)^2=0
又因为(2x-1)^2>=0,(3x-y)^2>=0,
所以只有(2x-1)^2=0,(3x-y)^2=0,即
x=1/2
y=3/2
代入(x+y)^13*x^10=(1/2+3/2)^13*1/2^10=2^13*1/2^10=(2*1/2)^10*2^3=8

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