Question

Please answer question no. 93
No spams!!

Answer 1

Given,
a² + 6b = -14 ⇒a² + 6b + 14 = 0 ----(1)
b² + 8c + 23 = 0 -----(2)
c² + 4a - 8 = 0 -----(3)

Adding equations (1), (2) and (3),
(a² + 6b + 14) + (b² + 8c + 23) + (c² + 4a - 8) = 0
arrange it in proper way,
(a² + 4a + 4) -4 + (b² + 6b + 9) - 9 + (c² + 8c + 16) - 16 +(14 + 23 - 8) = 0
⇒(a + 2)² + (b + 3)² + (c + 4)² - (4 + 9 + 16) + 29 = 0
⇒(a + 2)² + (b + 3)² + (c + 4)² = 0
What you think ?
of course , (a + 2) = 0 ⇒ a = -2
(b + 3) = 0 ⇒b = -3
(c + 4) = 0 ⇒c = -4

Now, ab + bc + ca = (-2)(-3) + (-3)(-4) + (-4)(-2)
= 6 + 12 + 8 = 26
Option (1) is correct