Question

Va rog daca se poate sa ma ajutati cu ceva idei pentru a rezolva problema din imagine, la nivel de clasa a patra (fara metoda algebrica)! Va multumesc!

Answer 1

 

$\displaystyle\bf\\2\times\overline{ab}\times \Big(3\times \overline{ab}-55\Big)=\overline{ab0}\\\\In~dreapta~egalului~avem:\\\overline{ab0}=\overline{ab}\times10\\\\In~stanga~egalului~avem:\\2\times\overline{ab}\times \Big(3\times \overline{ab}-55\Big) =\overline{ab}\times 2\times\Big(3\times \overline{ab}-55\Big)$

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$\displaystyle\bf\\Rezulta~egalitatea:\\\\\overline{ab}\times \underbrace{2\times\Big(3\times \overline{ab}-55\Big) }_{=10}=\overline{ab}\times10\\\\\\\implies 2\times\Big(3\times \overline{ab}-55\Big)=10\\\\2\times \underbrace{\Big(3\times \overline{ab}-55\Big)}_{=5}=2\times5\\\\\implies 3\times \overline{ab}-55=5\\\\\implies 3\times \overline{ab}=5+55\\\\\implies 3\times \overline{ab}=60\\\\\implies\overline{ab}=\frac{60}{3}\\\\\implies \boxed{\bf\overline{ab}=20}$