Question
Question: If a, b, c are real numbers forming an A.P. and 3 + a, 2 + b, 3 + c are in G.P., then minimum value...
If a, b, c are real numbers forming an A.P. and 3 + a, 2 + b,
3 + c are in G.P., then minimum value of ac is –
A
–4
B
–6
C
3
D
None
Answer
–6
Explanation
Solution
\ (2 + b )2 = (3 + a)(3 + c)
4 + b2 + 4b = 9 + 3(a + c) + ac
4 + b2 + 4b = 9 + 6b + ac
ac = b2 – 2b – 5
= (b – 1)2 – 6
ac ³ –6