Question

Добуток двох чисел дорівнює 120.Знайти ці числа, якщо одне із них на 2 менше, ніж друге.

Answer 1

Пусть $x$ и $y$ - загаданные числа, при чем $y\ \textless \ x$

$\left \{ {{x*y=120} \atop {x-y=2}} \right. \\\\ \left \{ {{x*y=120} \atop {x=y+2}} \right. \\\\ \left \{ {{(y+2)*y=120} \atop {x=y+2}} \right. \\\\ \left \{ {{y^2+2y-120=0} \atop {x=y+2}} \right. \\\\ \left \{ {{y^2+12y-10y-120=0} \atop {x=y+2}} \right. \\\\ \left \{ {{y(y+12)-10(y+12)=0} \atop {x=y+2}} \right. \\\\ \left \{ {{(y-10)(y+12)=0} \atop {x=y+2}} \right.$

$\left \{ {{y-10=0\ \ or\ \ y+12=0} \atop {x=y+2}} \right. \\\\ \left \{ {{y=10} \atop {x=10+2}} \right. \ \ or\ \ \left \{ {{y=-12} \atop {x=-12+2}} \right. \\\\ \left \{ {{x=12} \atop {y=10}} \right. \ \ or\ \ \left \{ {{x=-10} \atop {y=-12}} \right.$

Ответ: $(12;\ 10),\ \ (-10;\ -12)$