Question

is there anyone who can help me in this question..​

Answer 1

Answer:let us consider a and b  where a be any b postive number and  b is equal to 3 according to euclid division lemma

a=bq=r

where r is greater than or equal t zero ad less than b(0<r<b)

a=3q+r

s r is a integer greater than or equal to 0  and less than 3

Step-by-step explanation

case-1:when r=0 the equation become

a=3q

cubing both the side

a3=(3q)3

a3=27q3

a3=a(3q3)

a3=9m

where m =3q3

CASE-2: whenr=1 the equation become

a=3q+1

cubing both the side

a3=(3q+1)3

a3+(3q)3=1 3 + 3* 3q*(3q+1)

a3=27q3 +1+9q*(3q+1)

a3 =27q3+1+27q+9q

a3  =27q3+27q2+9q+1

a3=9(3q3+3q2+c)+1

as3=9m+1

where m=(3q3+3q2+q)

CASE-3: when r=2,the equation become

a=3q+2

cubing both the side

a3=(3q+2)3

a3=(3q)3+2 3 +3*3q*2(3q+1)

a3 = 27q3 +8+54q2+36q

a3=27q3+54q2+36q+8

a3=9(3q3+6q2+4q)+8

a3=9m+8

where m+(3q3+6q2+4q) therefore a can  be any of the form 9m or 9m+1or,9m+8

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