x^2﹢y^2-2x-6y﹢10
=(x²-2x+1)+(y²-6y+9)
=(x-1)²+(y-3)²
∵(x-1)²>=0 (y-3)²>=0
∴(x-1)²+(y-3)²>=0
即
x^2﹢y^2-2x-6y﹢10>=0