Question

Tee Euclid's division lemma to show that the cube of any positive integer is of the form 9m,
9m + 1 or 9m + 8.

Answer 1

Answer:

Step-by-step explanation:

a number can be written as 3n+1,3n+2, or 3n form

so  take number as x

first case-

take x=3n  taking cube on both sides

x^3=27n^3

x^3=9(3n^3)            take 3n^3=m

x^3=9m  

second case

take x=3n+1               cube on both sides

x^3=(3n+1)^3

x^3=27n^3+9n+27n^2  +1    (a+b)^3=a^3+b^3+3a^2b+3b^2a

x^3=9(3n^3+n+3n^2)+1                   put (3n^3+n+3n^2)=m

thus x^3=9m+1

further try yourself

Answer 2

Answer:

I hope it helps u...