If x and y are rational numbers and satisfy that the square of x plus 3 times the square of Y minus 12Y plus 12 is equal to 0, the value of x power of y can be obtained?

x^+3y^-12y+12=0
x^+3(y-2)^=0
Because the square is not negative
therefore
x=0
y=2
2^=1

If x + y = 3, the square of X - the square of y = 21, then the value of the fourth power of 3x - the third power of 17Y + 1 is

x²-y²=(x+y)(x-y)=3(x-y)=21
∴x-y=7
∵x+y=3
∴x=5,y=-2
3x^4-17y³+1
=3×625-17×(-8)+1
=1875+136+1
=2012

Given the square of X + 2x + the square of Y - 6x + 10 = 0, find the value of the power of y of X

Square of X + 2x + square of Y - 6x + 10 = 0
x²+2x+1+y²-6y+9=0
(x+1)²+(y-3)²=0
x+1=0,y-3=0
x=-1,y=3
X to the power of y = (- 1) to the power of 3 = - 1

Given the square of X + 2x + the square of Y - 6x + 4 = 0, find the Y power of X

Square of X + 2x + square of Y - 6x + 4 = 0
The square of X - 4x + 4 + y = 0
Square of (X-2) + square of y = 0
So, X-2 = 0, x = 2; y = 0
X to the power of y = 2 to the power of 0 = 1

If x and y are rational numbers and satisfy that the square of x plus 3 times the square of Y minus 12Y plus 12 is equal to 0, the value of x power of y can be obtained?