Question

a^2+9b^2+4a-6b+5=0

a=?
b=?

Answer 1

Răspuns:  a = - 2  si  b = 1/3

Explicație pas cu pas:

a² + 9 b² + 4 a - 6 b + 5 = 0

→ il scriu pe 5 ca suma: 1 + 4

( a² + 4 a + 4) + ( 9 b² - 6 b + 1 ) = 0

( a + 2 )² + ( 3 b - 1 )² = 0

a + 2 = 0   ⇒   a = - 2

3 b - 1 = 0 ⇒   b = 1/3

_________________

Verific:

( - 2)² + 9 × (1/3)² + 4 × ( - 2 ) - 6 × (1/3) + 5 =

= 4 + 9/9 - 8 - 2 + 5 =

= 5 - 10 + 5 =

= - 5 + 5 =

= 0

Answer 2

$\it a^2+9b^2+4a-6b+5=0 \Leftrightarrow (a^2+4a+4) +(9b^2-6b+1)=0\Leftrightarrow\\ \\ \Leftrightarrow (a+2)^2+(3b-1)^2=0 \Leftrightarrow \begin{cases} \it a+2=0 \Rightarrow a=-2\\ \\\it 3b-1=0 \Rightarrow b=\dfrac{1}{3} \end{cases}$