Grade 12th passAlgebra
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?
2 Answers
Ritesh Khatri
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
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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