Question

Найдите числа сумма которых ровна 20 а произведение 75

Answer 1

$\left \{ {{x+y=20} \atop {x*y=75}} \right. \\\left \{ {{x=20-y} \atop {(20-y)y=75}} \right. \\-y^{2} +20y=75\\-y^{2} +20y-75=0 |*(-1)\\y^{2} -20y+75=0\\D= (-20)^{2} -4*75=400-300=100\\y_{1} =\frac{20+\sqrt{100} }{2} =\frac{20+10}{2} =15\\y_{2}=\frac{20-\sqrt{100} }{2} =\frac{20-10}{2} =5\\x_{1}=20-15=5\\x_{2}=20-5=15\\Otvet: 15, 5$