$\text{a)x²+20+9y²+8x-12y=0}$
$\text{⇒ x²+8x+16+(3y)²-2.3.2y+4=0}$
$\text{⇒ (x+4)²+(3y-2)²=0}$
$\text{(x+4)²+(3y-2)²≥ 0}$
$\text{⇒(x+4)²=0 và (3y-2)²=0}$
$\left \{ {{(x+4)²=0} \atop {(3y-2)²=0}} \right.$
⇔$\left \{ {{x+4=0} \atop {3y-2=0}} \right.$
⇔$\left \{ {{x=-4} \atop {3y-2=\frac{2}{3}}} \right.$
b ) $\text{x²+9y²−12y+29−10x = 0}$
$\text{⇔(x²−10x+25)+(9y²−12y+4 )=0}$
$\text{⇔(x²−2.x.5+5²)+[(3y)²−2.3y.2+2²]=0}$
$\text{⇔(x−5)²+(3y−2)²=0}$
$\text{(x−5)²+(3y−2)²≥ 0}$
$\text{⇒(x−5)²=0 và (3y−2)²=0}$
$\left \{ {{(x−5)²=0} \atop {(3y-2)²=0}} \right.$
⇔$\left \{ {{x-5=0} \atop {3y-2=0}} \right.$
⇔$\left \{ {{x=5} \atop {3y-2=\frac{2}{3}}} \right.$
