1.
2a^2+25b^2+5(2a+5)-10ab=0 <=> (a^2-10ab+25b^2)+(a^2+10a+25)=0 <=> (a-5b)^2+(a+5)^2=0 <=> a-5b=0 si a+5=0.
a+5=0 => a=-5.
a-5b=0 => b=a/5=-5/5=-1.
In concluzie, a=-5 si b=-1.
2.
5x^2+9y^2-6x(2-y)+9=0 <=> (4x^2-12x+9)+(x^2+6xy+9y^2)=0 <=> (2x-3)^2 +(x+3y)^2=0 <=> 2x-3=0 si x+3y=0
2x-3=0 => x=3/2.
x+3y=0 => y=-x/3=-(3/2)/3=-1/2.
In concluzie, x=3/2 si y=-1/2.
PS: am presupus ca a,b si x,y sunt numere reale (deoarece nu s-a specificat)
