Question

1) x(x - 5) = 24; 2) x(x + 7) = 78; 3) x(x + 8) =105.​

Answer 1

Ответ:

$-3 \ ; \ 8 \ ;$

$-13 \ ; \ 6 \ ;$

$-15 \ ; \ 7 \ ;$

Пошаговое объяснение:

Решаем уравнения при помощи теоремы Виета:

$1) \ x(x-5)=24;$

$x^{2}-5x-24=0;$

$\displaystyle \left \{ {{x_{1}+x_{2}=-(-5)} \atop {x_{1} \cdot x_{2}=-24}} \right. \Leftrightarrow \left \{ {{x_{1}+x_{2}=5} \atop {x_{1} \cdot x_{2}=-24}} \right. \Leftrightarrow \left \{ {{x_{1}=-3} \atop {x_{2}=8}} \right. ;$

$2) \ x(x+7)=78;$

$x^{2}+7x-78=0;$

$\displaystyle \left \{ {{x_{1}+x_{2}=-7} \atop {x_{1} \cdot x_{2}=-78}} \right. \Leftrightarrow \left \{ {{x_{1}=-13} \atop {x_{2}=6}} \right. ;$

$3) \ x(x+8)=105;$

$x^{2}+8x-105=0;$

$\displaystyle \left \{ {{x_{1}+x_{2}=-8} \atop {x_{1} \cdot x_{2}=-105}} \right. \Leftrightarrow \left \{ {{x_{1}=-15} \atop {x_{2}=7}} \right. ;$