a2 + b2 + c2 + 4a + 6b + 13 = 0 find a + b + c + 5

The correct answer is option I

a² + b² + c² + 4a + 6b + 13 = 0

⇒ a² + b² + c² + 2 (2a + 3b) + (4 + 9) = 0

⇒ [a² + 2(2a) + 4] + [b² + 2(3b) + 9] + c² = 0

⇒ [(a + 2)²] + [(b + 3)²] + c² = 0

{when x² + y² + z² = 0, then x = 0, y = 0 & z = 0}

Therefore, we can say,

⇒ (a + 2)² = 0  ⇒ a = -2

⇒ [(b + 3)²] = 0 ⇒ b = -3

⇒ c² = 0 ⇒ c = 0

Put in find.

⇒ a + b + c + 5 = -2 -3 + 0 + 5 = 0

 

Alternate:

Here we can write the statement like this:

a² + b² + c² = 2 (-2a - 3b) - 13

So, here the coefficient of a and b will be the values of a and b.

and c = 0 (∵ coefficient of c is not given)

So, a = -2, b = -3 & c = 0

Put in find.

⇒ a + b + c + 5 = -2 -3 + 0 + 5 = 0