Question

use euclid division lemma to show that cube of any positive integer is of the form 9m,9m+1,9m+8​

Answer 1

Step-by-step explanation:

a=bq+r a=3q+r

a=3q+r (r=0) a=3q+1

a=3q+0

a=3q

a=3q

a3=(3q)3

a3=27q3

a3=9(3q3)

a3=9m (3q3=m)

a=3q+1

a3=(3q+1)3

=(3q)3+(1)3+3(3q)(1)(3q+1)

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

=27q3+1+27q2+9q

=27q3+27q2+9q+1

=9(3q3+3q+q)+1

*a3=9m+1

a=3q+2

a3=(3q+2)3

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

a3=27q3+8+18q(3q+2)

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

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

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

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

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