1.

Four different integers form an increasing A.P .One of these numbers is equal to the sum of the squares of the other three numbers. Then The product of all numbers isA. `-2`B. 1C. 0D. 2

Answer» Correct Answer - C
Let the four integers be a-d,a,a+d, and a+2d, where a and d are integers and `dgt0`. Now,
`a+2d=(a-d)^(2)+a^(2)+(a+d)^(2)`
or `2d^(2)-2d+3a^(2)-a=0` (1)
`therefored=1/2[1pmsqrt(1+2a-6a^(2))]` (2)
Since d is a positive integer, so
`1+2a-6a^(2)gt0`
or `6a^(2)-2a-1lt0`
or `(1-sqrt7)/6ltalt(1+sqrt7)/6`
or a=0 (`because` a is an integer)
Hence, from (2),
d=1 or 0
But since `dgt0`,
`therefore` d=1
Hence, the four numbers are -1,0,1,2.


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