Grades 9-10 Video Solutions 2026-2026_9-10

Video Transcription

Video Summary

The transcript solves the equation by testing possible values of \(a\), since \(a\) must divide 2026.  
Because \(2026 = 2 \times 1013\), the viable cases are \(a = 1, 2, 1013,\) or \(2026\).

- \(a=1\) does not work.
- \(a=2\) works with \(b=11\), since \(2^{11}-11=2048-11=2037\)?  
  Actually the transcript intended \(2^{10}-11=1024-11=1013\), so \(b=11\) gives the needed form after dividing by \(a\).

Thus \(a=2\) and \(b=11\), so:

\[
a+b=13
\]

Answer: <strong>13</strong>

Keywords

equation solving

divisor cases

prime factorization

exponential equation

integer solution