Question
Question: If a, b, c, d are distinct integers in A.P. such that d = a<sup>2</sup> + b<sup>2</sup> + c<sup>2</...
If a, b, c, d are distinct integers in A.P. such that
d = a2 + b2 + c2 then a + b + c + d is –
A
0
B
1
C
2
D
None of these
Answer
2
Explanation
Solution
Let common difference be k. (k Î I)
̃ d = a + 3k = a2 + (a +k)2 + (a + 2k)2
̃ 5k2 + 3 (2a –1) k + 3a2 – a = 0
k Î R ̃ D ³ 0
̃ 9(2a –1)2 –4.5 (3a2 – a) ³ 0
̃ 24a2 +16a – 9 £ 0 ̃ a = –1, 0
If a = 0 ̃ k = 0, 3/5 ̃ k = 0
which is not possible.
Hence a = –1 ̃ k = 1
So a + b + c + d = 2