Question

if can do this do
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Answer 1

11(1+2) + 12 (2+1)

= 11³ + 12³

= 1331 + 1728

= 133 (10) + 1 + 1728

=133(10) + 1729

=133(10) + 133(13)

=133 (26)

Assume it is true for a natural number k. Prove it is true for the number k + 1:

True for k:

11(k+2) + 12(2k+1) = 133(m), where mis

an integer.

Fork +1:

11k+1+2 + 122(k+1)+1

= 11k+2 x 11+122k+2+1 =11(k+ 2) × 11 + 12(2k + 1) × 12²

=11 × 11k+² + (11 +133) × 12²k+1

=11(11k+2 + 12²k+1) + 133 × 12²k+1

=11(133m) + 133 × 12²k+1

B 133(11m + 12(2k+1)) hence it is divisible

by 133.