Question

Determinati numerele reale a si b, stiind ca a patrat + b patrat - 2a + 6b + 10 = 0.
Cum demonstrez care sunt numerele?

Answer 1

$a^{2} + b^{2} -2a+6b+10= a^{2} -2a+1+ b^{2} +6b+9=$
$(a-1)^{2}+ (b+3)^{2}=0$
Avem suma a doua patrate perfecte egala cu 0 deci cele doua patrate perfecte vor fi 0,
adica (a-1)² =0, a=1; (b+3)²=0, b=-3