Question

Sa se determine ab par,a mai mic decat b,daca 40(a,b+b,a) este un patrat perfect

Dau coroana

Answer 1

$40\cdot(a,b+b,a)= \\ \\ \\ 40\cdot( \dfrac{ab}{10}+ \dfrac{ba}{10})= \\ \\ \\ \dfrac{40}{1}\cdot \dfrac{ab+ba}{10}= \\ \\ \\ 4\cdot(ab+ba)= \\ \\ \\ 4\cdot(10a+b+10b+a)= \\ \\ \\ 4\cdot(11a+11b)= \\ \\ \\ 44(a+b)= \\ \\ \\ {2}^{2}\cdot11\cdot(a+b)= \\ \\ \\ {11}^{2}=pp=>a+b=11 \\ \\ \\ a=3,b=8 ; a=5,b=6 \\ \\ \\ ab=38,56$

Succes!