Question

а) 5х2 – 10 = 0;

б) х2 + 4х = 0;

в) 3х2 + 7х + 2 = 0;

г) х2 – 8х + 12 = 0;

д) х2 + х + 3 = 0

е) (2х - 1)(2х + 1) – (х - 3)(х + 1) = 18.

Срочно! Решите пожалуйста(

Answer 1

Решение:
$5 {x}^{2} - 10 = 0 \ 5 {x}^{2} = 10 \ {x}^{2} = 2 \ x = sqrt{2}$

${x}^{2} + 4x = 0 \ x(x + 4) = 0 \ x_1 = 0 \ x_2 = - 4$

$3 {x}^{2} + 7x + 2 = 0 \ D = 49 - 4 times 3 times 2 = 49 - 24 = 25 \ x_1 = frac{ - 7 + 5}{6} = - frac{1}{3} \ x_2 = frac{ - 7 - 5}{6} = - 2$

${x}^{2} - 8x + 12 = 0 \ D_1 = 16 - 12 = 4 \ x_1 = 4 + 2 = 6 \ x_2 = 4 - 2 = 2$

${x}^{2} + x + 3 = 0 \ D = 1 - 12 < 0$
Корней нет

$(2x - 1)(2x + 1) - (x - 3)(x + 1) = 18 \ 4 {x}^{2} - 1 - {x}^{2} - x + 3x + 3 = 18 \ 3 {x}^{2} + 2x - 16 = 0 \ D_1 = 1 + 48 = 49 \ x_1 = frac{ - 1 + 7}{3} = 2 \ x_2 = frac{ - 1 - 7}{3} = - 2 frac{2}{3}$
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Примечание:

$D=b^{2}-4ac\x_{1,2}=frac{-bpm sqrt{D}}{2a}\\D_1 = k^{2}-ac\x_{1,2}=frac{-kpm sqrt{D_1}}{a}\k=frac{1}{2}b$

Answer 2

Спасибо:**