Question

не вычисляя корней уравнения х²-3х -10=0 найдите х²\1+х2\2 быстрее ​

Answer 1

$\displaystyle\bf\\x^{2} -3x-10=0\\\\Teorema \ Vieta\\\\x_{1} +x_{2} =3\\\\x_{1} \cdot x_{2} =-10\\\\(x_{1} +x_{2})^{2} =3^{2} \\\\x_{1}^{2} +2x_{1} x_{2}+x_{2}^{2} =9\\\\x_{1}^{2} +x_{2}^{2} =9-2x_{1} x_{2}=9-2\cdot(-10)=9+20=29\\\\Otvet:x_{1}^{2} +x_{2}^{2} =29$