已知13X^2-6XY+Y^2-4x+1=0,求(x+y)^13乘以x^10

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已知13X^2-6XY+Y^2-4x+1=0,求(x+y)^13乘以x^10

已知13X^2-6XY+Y^2-4x+1=0,求(x+y)^13乘以x^10
已知13X^2-6XY+Y^2-4x+1=0,求(x+y)^13乘以x^10

已知13X^2-6XY+Y^2-4x+1=0,求(x+y)^13乘以x^10
把13X^2-6XY+Y^2-4x+1=0配方,得
13X^2-6XY+Y^2-4x+1=0
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

13X^2-6XY+Y^2-4x+1=0
9X^2-6XY+Y^2 + 4X^2-4x+1=0
(3x-y)^2+(2x-1)^2=0
由非负性
3x-y=0
2x-1=0
解得
x=1/2
y=3/2
(x+y)^13乘以x^10
=2^13 * (1/2)^10
=2^3
=8

13X^2-6XY+Y^2-4x+1=0
9x^2-6xy+y^2+4x^2-4x+1=0
(3x-y)^2+(2x-1)^2=0
x=1/2
y=3/2
(x+y)^13乘以x^10=(1/2+3/2)^13*1/2^10=2^13*1/2^10=(2*1/2)^10*1/2^3=1/8

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