初一数学题~急1.已知13X的2次方-6XY+Y的2次方-4X+1=0,求(XY-X的2次方)的5次方的值2.K为何值时

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
x^2-4xy+4y^2-10x+20y+k^2+9
=(x-2y)^2-10(x-2y)+(k^2+9)
k^2+9=(10/2)^2=25
k^2=16
k1=4,k2=-4.
k为4或-4时,x^2-4xy+4y^2-10x+20y+k^2+9是一个完全平方式.
证明:(x^2 -4)(x^2-10x+21)+100
=(x+2)(x-2)(x-3)(x-7)+100
=(x^2-5x-14)(x^2-5x+6)+100
=(x^2-5x)^2-8(x^2-5x)+16
=(x^2-5x-4)^2
因为(x^2-5x-4)^2大于等于0,
所以(x^2 -4)(x^2-10x+21)+100是非负数

2.K=五分之三（X-2Y）
3.