Question

Express 12 cube as the sum of odd natural number

Answer 1

12^3 =(5+7)^3

(5+7)^3=5^3+7^3+3^5^7(5+7)

= 125+343+525+735

In this way cube of 12 may be expressed as the sum of odd numbers

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there are a lot and I mean a lot of ways to do that,

easiest would be the following,

12^3=1728

you could divide 1728 by 2 giving

864,

so 864 + 864=12^3

add 1 and subtract 1 to left hand side

(864–1) + (864+1) =12^3

863 + 865 =12^3

so there you have it.

P.S. my way of doing it

(Using ramanujan’s number, since I remember that everytime i hear 12^3 or any of the others)

12^3 +1^3 = 9^3 + 10^3

12^3 +1 = 729 +1000

12^3 = 729 + (1000–1)

12^3 = 729 + 999

Answer 2

Answer:

hope it helps you mate all the best