Question

sovle the problem or sum​

Answer 1

Step-by-step explanation:

Let x be the number

On dividing x by 3, let y be the quotient and z be the remainder. So, By Euclid's division lemma, we have :

x = 3y + z, where 0 ≤ z < 3

Now,

Cubing both sides :-

(x)³ = (3y + z)³

» x³ = 27y³ + 27y²z + 9yz² + z³ ...... (i) (where 0 ≤ z < 3)

Now,

Case I :-

When z = 0

Substituting value of z on equation (i)

x³ = 27y³

= 9(3q³) = 9m, where m = 3q³

Case II :-

When z = 1

Substituting value of z on equation (i)

x³ = 27y³ + 27y² + 9y + 1

= 9(3y³ + 3y² + y) + 1 = 9m + 1,

where m = 3y³ + 3y² + y

Case III :-

When z = 2

Substituting value of z on equation (i)

x³ = 27y³ + 54y² + 36y + 8

= 9(3y³ + 6y² + 4y) + 8 = 9m + 8,

where m = 3y³ + 6y² + 4y

Hence,

The cube of any positive integer is of the form 9m or 9m + 1 or 9m + 8.

Answer 2

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n tricky u r

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