Question

Determinați numerele naturale de forma abc care verifică relația ab4-b4+5c=752​

Answer 1

 

$\displaystyle\bf\\\overline{ab4}-\overline{b4}+\overline{5c}=752\\\\100a+\underline{(10b+4)}-\underline{(10b+4)}+10\times5+c=100\times7+10\times5+2\\\\100a+10\times5+c=100\times7+10\times5+2\\\\a=7\\b\in{0;~1;~2;~3;~4;~5;~6;~7;~8;~9}\\c=2\\\\\boxed{\bf\overline{abc}\in\{702;~712;~722;~732;~742;~752;~762;~772;~782;~792\}}$