Question

Даю сто балів. Зробіть будь-ласка терміново

Answer 1

а)

$\frac{ {x}^{2} + 2x }{3} = \frac{4x + 1}{5} \\ 5( {x}^{2} + 2x) = 3(4x + 1) \\ 5 {x}^{2} + 10x = 12x + 3 \\ 5 {x}^{2} + 10x - 12x - 3 = 0 \\ 5 {x}^{2} - 2x - 3 = 0 \\ D = ( - 2) {}^{2} - 4 \times 5 \times ( - 3) = \\ 4 + 60 = 64 \\ x_{1} = \frac{2 + 8}{5 \times 2} = \frac{10}{10} = 1\\ x_{2} = \frac{2 - 8}{5 \times 2} = - \frac{6}{10} = - 0.6$

б)

$\frac{x + 1}{3} + \frac{ {x}^{2} - 1}{2} = \frac{1}{3} \: \: \: | \times 6 \\ 2(x + 1) + 3( {x}^{2} - 1) = 2 \\ 2x + 2 + 3 {x}^{2} - 3 - 2 = 0 \\ 3 {x}^{2} + 2x - 3 = 0 \\ D = {2}^{2} - 4 \times 3 \times ( - 3) = \\ 4 + 36 = 40 \: \: ( \sqrt{D} = 2 \sqrt{10} ) \\ x_{1} = \frac{ - 2 + 2 \sqrt{10} }{3 \times 2} = \frac{2( - 1 + \sqrt{10} ) }{3 \times 2} = \\ \frac{ - 1 + \sqrt{10} }{3} \\ x_{2} = \frac{ - 2 - 2 \sqrt{10} }{3 \times 2} = \frac{2( - 1 - \sqrt{10} ) }{3 \times 2} = \\ \frac{ - 1 - \sqrt{10} }{3}$