849° Вправа 849Алгебра 8 клас Тарасенкова 2025 · § 21 · стор. 255

849. Розв’яжіть рівняння:

1) ${\displaystyle x^4+x^2-20=}$${\displaystyle 0}$;

${\displaystyle t=}$${\displaystyle x^2}$, ${\displaystyle t\ge 0}$;

${\displaystyle t^2+t-20=}$${\displaystyle 0}$;

${\displaystyle t_1+t_2=}$${\displaystyle -1}$; ${\displaystyle t_1\cdot t_2=}$${\displaystyle -20}$;

${\displaystyle t_1=}$${\displaystyle 4}$;

${\displaystyle t_2=}$${\displaystyle -5}$ — не задовольняє ${\displaystyle t\ge 0}$;

${\displaystyle x^2=}$${\displaystyle 4}$;

${\displaystyle x_{1,2}=}$${\displaystyle \pm 2}$;

2) ${\displaystyle x^4-9x^2+20=}$${\displaystyle 0}$;

${\displaystyle t=}$${\displaystyle x^2}$, ${\displaystyle t\ge 0}$;

${\displaystyle t^2-9t+20=}$${\displaystyle 0}$;

${\displaystyle t_1+t_2=}$${\displaystyle 9}$; ${\displaystyle t_1\cdot t_2=}$${\displaystyle 20}$;

${\displaystyle t_1=}$${\displaystyle 4}$; ${\displaystyle t_2=}$${\displaystyle 5}$;

${\displaystyle x^2=}$${\displaystyle 4}$ або ${\displaystyle x^2=}$${\displaystyle 5}$;

${\displaystyle x_{1,2}=}$${\displaystyle \pm 2}$; ${\displaystyle x_{3,4}=}$${\displaystyle \pm \sqrt{5}}$;

3) ${\displaystyle x^4-5x^2+4=}$${\displaystyle 0}$;

${\displaystyle t=}$${\displaystyle x^2}$, ${\displaystyle t\ge 0}$;

${\displaystyle t^2-5t+4=}$${\displaystyle 0}$;

${\displaystyle t_1+t_2=}$${\displaystyle 5}$; ${\displaystyle t_1\cdot t_2=}$${\displaystyle 4}$;

${\displaystyle t_1=}$${\displaystyle 1}$; ${\displaystyle t_2=}$${\displaystyle 4}$;

${\displaystyle x^2=}$${\displaystyle 1}$ або ${\displaystyle x^2=}$${\displaystyle 4}$;

${\displaystyle x_{1,2}=}$${\displaystyle \pm 1}$; ${\displaystyle x_{3,4}=}$${\displaystyle \pm 2}$;

4) ${\displaystyle x^4+11x^2+18=}$${\displaystyle 0}$;

${\displaystyle t=}$${\displaystyle x^2}$, ${\displaystyle t\ge 0}$;

${\displaystyle t^2+11t+18=}$${\displaystyle 0}$;

${\displaystyle t_1+t_2=}$${\displaystyle -11}$; ${\displaystyle t_1\cdot t_2=}$${\displaystyle 18}$;

${\displaystyle t_1=}$${\displaystyle -2}$; ${\displaystyle t_2=}$${\displaystyle -9}$;

${\displaystyle t_1<0}$, ${\displaystyle t_2<0}$ — коренів немає.