Answer to Question #13400 in Algebra for pankaj bhist
The smaller of these two squares is obtained by subtracting k from n and the
larger one is obtained by adding l to n. Prove that n − kl is a perfect square.
n-a² = k,& (1)
(a+1)² –n = l.& (2)
Adding (1) and (2):
k + l = 2a + 1,
l = 2a + 1 - k.
n-kl = (a²+k) – k(2a+1-k)
= a² + k – 2ak –k + k²
= a² – 2ak + k² = (a-k)².
Hence proved that n-kl is a perfect square.
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