Question

Найдите ошибку. почему получилось что в квадратном уравнении нет решения? ​

Answer 1

$\left \{ {{x^{2}+y^{2}=13^{2}} \atop {\frac{1}{2}xy=30}|*4} \right.\\\\+\left \{ {{x^{2}+y^{2}=169} \atop {2xy=120}} \right.\\-------\\x^{2}+2xy+y^{2}=289\\\\(x+y)^{2}=289\\\\x+y=\pm17$

$1)\left \{ {{x+y=17} \atop {xy=60}} \right.\\\\\left \{ {{y=17-x} \atop {xy=60}} \right. \\\\x(17-x)=60\\\\17x-x^{2} -60=0\\\\x^{2}-17x+60=0\\\\x_{1}=5\\\\x_{2}=12-teorema.Vieta\\\\y_{1}=17-5=12\\\\y_{2} =17-12=5$

$2)\left \{ {{x+y=-17} \atop {xy=60}} \right.\\\\\left \{ {{y=-x-17} \atop {xy=60}} \right.\\\\x(-x-17)-60=0\\\\-x^{2}-17x-60=0\\\\x^{2}+17x+60=0\\\\x_{1} =-5\\\\x_{2}=-12-teorema.Vieta\\\\y_{1}=-(-5)-17=5-17=-12\\\\y_{2}=-(-12)-17=12-17=-5\\\\Otvet:\boxed{(5;12),(12;5),(-5;-12),(-12;-5)}$