If a, b, c, d are distinct integers in A. P. Such that `d=a^2+b^2+c^2` – InterviewSolution

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1.	If a, b, c, d are distinct integers in A. P. Such that `d=a^2+b^2+c^2`, then a + b + c + d is
Answer» Correct Answer - 2 `a+3k=a^(2)+(a+k)^(2)+(a+2k)^(2)` (1) (where k is the common difference of A.P) `rArr5k^(2)+3(2a-1)k+3a^2)-a=0` (2) `rArr9(2a-1)^(2)-20(3a^(2)-a)ge0(becausek is "real")` `rArr24a^(2)+16a-9le0` `rArr-1/3-(sqrt(70))/12ltalt-1/3+(sqrt(70))/12` `rArrk=0`,3/5 [Not possible] When a=-1 `5k^(2)-9k+4=0` `rArrk=1,4/5rArrk=1` (since k is an integer) `thereforea=-1,b=0,c=1,d=2` `rArra+b+c+d=2`

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