Practicing Success
a2 + b2 + c2 + 4a + 6b + 13 = 0 find a + b + c + 5 |
0 -2 -3 -5 |
0 |
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 |