Let the number n be between a^2 and (a+1)^2
As per given condition
n- a^2 = k\cdots(1)
(a+1)^2 –n = l\cdots(2)
Adding (1) and (2)
k + l = 2a + 1
or l = 2a + 1 - k
now
n- kl = (a^2+k) – k(2a+1-k)
= a^2 + k – 2ak –k + k^2 = a^2 – 2ak + k^2 = (a-k)^2
Hence proved
No comments:
Post a Comment