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find the largest n such that n+10 divides n^3 + 100..

find the largest n such that n+10 divides n^3 + 100.. 

Grade:10

1 Answers

APURV GOEL
39 Points
9 years ago

Here n3 + 100 = n3 + 1000 - 900

                     = (n + 10)(n2 + 100 + 10n) - 900

here (n + 10)(n2 + 100 + 10n) is divisible by n + 10 so now question reduces to 900 should be divisible by n+10

Let us say 900 = (n + 10) x (some natural no.)

 for largest value of n natural no. is 1.

 Hence 900 = n + 10

so n = 890

This is your ans.

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