Question

If a^2+b^2= 4b+6a-13
Then what osbthe value of a+ b

Answer 1

Answer:

The value of a + b would be 5.

Step-by-step explanation:

Given expression,

$a^2 + b^2 = 4b + 6a- 13$

$a^2 + b^2 - 4b - 6a + 13 = 0$

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

By using (a-b)² = a² - 2ab + b²

We get,

$(a-3)^2 + (b-2)^2 = 0$

Since, x² + y² = 0 iff x = y = 0 ∀ x, y ∈ R

Thus, a - 3 = 0 ⇒ a = 3  and b - 2 = 0  ⇒ b = 2

Hence,

a + b = 3 + 2 = 5