[tex]\displaystyle\bf\\4a^2+9b^2-12a-6b+10=0\\\\10=9+1\\\\4a^2+9b^2-12a-6b+9+1=0\\\\(4a^2-12a+9)+(9b^2-6b+1)=0\\\\((2a)^2-2\times2a\times3+3^2)+((3b)^2-2\times3b\times1+1^1)=0\\\\(2a-3)^2+(3b-1)^2=0\\\\Avem~suma~de~2~patrate~perfecte=0\\\\(2a-3)^2=0~~~~~si~~~~~(3b-1)^2=0\\\\~~~~~2a-3=0~~~~~si~~~~~3b-1=0\\\\~~~~~~~~~~~2a=3~~~~~si~~~~~3b=1\\\\~~~~~~~~~~~~a=\frac{3}{2}~~~~~si~~~~~b=\frac{1}{3}[/tex]
