已知13x²-6xy+y²-4x+1=0,求(xy-x²)的5次方

已知13x²-6xy+y²-4x+1=0,求(xy-x²)的5次方
已知13x²-6xy+y²-4x+1=0,求(xy-x²)的5次方

已知13x²-6xy+y²-4x+1=0,求(xy-x²)的5次方
13=9+4
所以(9x²-6xy+y²)+(4x²-4x+1)=0
(3x-y)²+(2x-1)²=0
平方相加为0则两个都等于0
所以3x-y=0,2x-1=0
x=1/2,y=3/2
所以(xy-x²)的5次方
=(3/4-1/4)的5次方
=1/32

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
3x-y=0,
2x-1=0,
x=0.5
y=3*0.5=1.5
(xy-x^2)^5
=(0.5*1.5-0.5^2)^5
=(0.5(1.5-0.5))^5
=0.5^5
=1/32