1086 Вправа 1086Алгебра 8 клас Бевз 2025 · § 21 · стор. 204

1086. Розклади на множники тричлен. а) 0,2n² + 0,8n − 12; б) (4/49)x² + 1 5/7 x + 9; в) m² − 3√2m + 4.

а) ${\displaystyle 0,2n^2+0,8n-12=}$${\displaystyle 0,2(n^2+4n-60)}$;

${\displaystyle n^2+4n-60}$: ${\displaystyle n_1+n_2=}$${\displaystyle -4}$;

${\displaystyle n_1{n}_2=}$${\displaystyle -60}$ → ${\displaystyle n_1=}$${\displaystyle 6,n_2=}$${\displaystyle -10}$;

${\displaystyle n^2+4n-60=}$${\displaystyle \left(n-6\right)\left(n+10\right)}$;

${\displaystyle 0,2n^2+0,8n-12=}$${\displaystyle 0,2\left(n-6\right)\left(n+10\right)}$;

б) ${\displaystyle \frac{4}{49}{x}^2+1\frac{5}{7}x+9=}$${\displaystyle \frac{4}{49}{x}^2+\frac{12}{7}x+9}$;

${\displaystyle D=}$${\displaystyle {\left(\frac{12}{7}\right)}^2-4\cdot \frac{4}{49}\cdot 9=}$${\displaystyle \frac{144}{49}-\frac{144}{49}=}$${\displaystyle 0}$ — повний квадрат:

${\displaystyle {\left(\frac{2}{7}x\right)}^2+2\cdot \frac{2}{7}x\cdot 3+3^2=}$${\displaystyle {\left(\frac{2}{7}x+3\right)}^2}$;

в) ${\displaystyle m^2-3\sqrt{2}m+4}$: ${\displaystyle D=}$${\displaystyle 18-16=}$${\displaystyle 2}$;

${\displaystyle m_{1,2}=}$${\displaystyle \frac{3\sqrt{2}\pm \sqrt{2}}{2}}$;

${\displaystyle m_1=}$${\displaystyle 2\sqrt{2}}$;

${\displaystyle m_2=}$${\displaystyle \sqrt{2}}$;

${\displaystyle m^2-3\sqrt{2}m+4=}$${\displaystyle \left(m-2\sqrt{2}\right)\left(m-\sqrt{2}\right)}$.