Question

решить с помощью теоремы виета​

Answer 1

Ответ:

$2, \quad 7; \quad -4-\sqrt{31}, \quad -4+\sqrt{31};$

Объяснение:

$1. \quad x^{2}-9x+14=0;$

$\left \{ {{x_{1}+x_{2}=-(-9)} \atop {x_{1} \cdot x_{2}=14}} \right. \Leftrightarrow \left \{ {{x_{1}+x_{2}=9} \atop {x_{1} \cdot x_{2}=14}} \right. \Leftrightarrow \left \{ {{x_{1}=2} \atop {x_{2}=7}} \right. ;$

$2. \quad x^{2}+8x-15=0;$$\left \{ {{x_{1}+x_{2}=-8} \atop {x_{1} \cdot x_{2}=-15}} \right. \Leftrightarrow \left \{ {{x_{1}+x_{2}=-4+(-4)} \atop {x_{1} \cdot x_{2}=16-31}} \right. \Leftrightarrow \left \{ {{x_{1}+x_{2}=-4+(-4)} \atop {x_{1} \cdot x_{2}=(-4)^{2}-(\sqrt{31})^{2}}} \right. \Leftrightarrow \left \{ {{x_{1}+x_{2}=-4+(-4)} \atop {x_{1} \cdot x_{2}=(-4-\sqrt{31})(-4+\sqrt{31})}} \right. \Leftrightarrow$$\Leftrightarrow \left \{ {{x_{1}=-4-\sqrt{31}} \atop {x_{2}=-4+\sqrt{31}}} \right. ;$