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CBSE Class 10 Answered

Let Sn =n²+20n+12, n a positive integer. What is the sum of all possible values of n for which Sn is a perfect square?
Asked by vikasg13.hardware | 17 Jun, 2018, 07:46: AM
answered-by-expert Expert Answer

Let

n2+20n+12=u2

(n+10)2−88=u2

(n+10−u)(n+10+u)=88

As

88=88×1=44×2=22×4=11×8

Using each of the pair of factors of 88, we can get different values of n and u. Of all the values, we get n=3 and n=13 as positive integer solutions.

Thus, sum of all possible values of n is 3+13 = 16

Answered by Arun | 18 Jun, 2018, 12:46: PM

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