# Questions 3,4 and 5 only. . ...........................

Arun
25757 Points
4 years ago
Dear Pushkar

5.
We write 3a2 -  1 , As
= 3 (a2 -  1)+
= 3 k  +  2,  Here  k = a2 − 1.
And we know  that the square of an integer must either be of the form 3 k or 3k + 1.
Hence, 3a2  -  1 = 3k + 2 cannot be a perfect square.
we can also check for different value of a , As :
At a  =  1 , we get
3a2 -  1  =  3 ( 1 )2 - 1  =  2 , That is not a perfect square .
Or
At a  = 2 , we get
3a2 -  1  =  3 ( 2 )2 - 1  =  11 , That is not a perfect square .
Or
At a  =  5 , we get
3a2 -  1  =  3 ( 5 )2 - 1  =  74 , That is not a perfect square .
So,
we can say 3a2 - 1 never be a perfect square.