Question

aflati cel mai mare numar de gorma ab scris in baza 10 stiind ca ab(cu bara feasupra) pe4 =ba(bara deasupra) pe 7.

Answer 1

$\frac{10a+b}{4} = \frac{10b+a}{7}$
7(10a+b)=4(10b+a)
70a+7b=40b+4a
70a-4a=40b-7b
66a=33b
2a=b
a=1;b=2
a=2;b=4
a=3;b=6
a=4;b=8
cel mai mare nr va fi 48

Answer 2

$ab=10a+b\\ba=10b+a\\\frac{10a+b}{4}=\frac{10b+a}{7}\\produsul\ mezilor=produsul\ extremilor\\Se\ inmulteste\ prin\ diagonale\\7*(10a+b)=4*(10b+a)\\Se\ inmultesc\ termenii\ din\ paranteza\ cu\ factorul\ 1\\7*10a+7*b=4*10b+4*a\\70a+7b=40b+4a\\70a-4a=40b-7b\\66a=33b\\Se\ da\ factor\ comun\ 33\\33*2a=33*b\\2a=b\\a=numar\ de\ o\ cifra\\b=numar\ de\ o\ cifra\\ a\neq0\\b\neq0\\a=1;b=2\\a=2;b=4\\ a=3;b=6\\a=4;b=8\\ab\ maxim=48$