b= n^3 +2 n^2 = n^2(n+2) such that b makes for a perfect square. both n^2 and n+2 have to be odd. so n can be an odd natural number such that b is a perfect square. so the smallest b is 441 only. But I still think it should be mentioned as perfect square.
If we have to find only 1 value
ReplyDelete441=7^3+ 2(7)^2 satisfies the condition.
Find the smallest b ..
ReplyDeleteThe question is incomplete. sorry!
The smallest value of b will then be 3 as the question does not say perfect square.
ReplyDelete3= (1)^3 + 2 (1)^2
what does odd square mean, if it is not perfect square????
ReplyDeleteb= n^3 +2 n^2
ReplyDelete= n^2(n+2)
such that b makes for a perfect square. both n^2 and n+2 have to be odd.
so n can be an odd natural number such that b is a perfect square.
so the smallest b is 441 only.
But I still think it should be mentioned as perfect square.
yaar odd square means perfect square,
ReplyDeletethere is nothing called an imperfect square!