Squares Of Numbers

Algebra Level 2

A number n − 1 n-1 's square is 974169 974169 . The square of n + 1 n+1 is 978121 978121 . Find n n without a calculator.


The answer is 988.

Just C by Just C , 15, Hong Kong

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1 solution

Just C
Oct 6, 2020

Because ( n − 1 ) 2 = n 2 − 2 n + 1 (n-1)^{2} = n^2 - 2n + 1 and ( n + 1 ) 2 = n 2 + 2 n + 1 (n+1)^{2} = n^2 + 2n + 1 , ( n + 1 ) 2 − ( n − 1 ) 2 = n 2 + 2 n + 1 − n 2 − ( − 2 n ) − 1 = 4 n (n+1)^2 - (n-1)^2 = n^2 + 2n + 1 - n^2 - (-2n) - 1 = 4n . Therefore, n = 978121 − 974169 4 = 3952 4 = 988 n = {{978121-974169} \over {4}}={{3952}\over {4}}=988

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