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3^9+3^12+3^15+3^n is a perfect cube ,n is a natural number then find n?

3^9+3^12+3^15+3^n is a perfect cube ,n is a natural number then find n?

Grade:12th pass

2 Answers

Ritesh Khatri
76 Points
3 years ago
if we write cube of (3^3 + 3^5)
we will get 3^9 + 3^15 + 3^12 + 3^14
on comparing given expression with this we get n = 4
naveen
15 Points
10 months ago

39( 1 + 33 + 36 + 3n-9) = k3

( 1 + 33 + 36 + 3n-9) has to be a perfect cube

( 1 + 27 + 729 + 3n-9) has to be a perfect cube

(757 + 3n-9) has to be a perfect cube

103 = 1000 = 757 + 243 = 757 + 35

Hence, n = 14 

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