Question

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ПОМОГИТЕ

Answer 1

$(6x + 5) {}^{2} + 30 = 31x(x + 3) + 2x \\ 36x {}^{2} + 60x + 25 + 30= 31 {x}^{2} + 93x + 2x \\ 36 {x}^{2} + 60x + 55 - 31 {x}^{2} - 95x = 0 \\ 5 {x}^{2} - 35x + 55 = 0 \\ {x}^{2} - 7x + 11 = 0$

По теореме Виета:

${x}^{2} + bx + c = 0 \\ x _{1} + x_{2} = - b \\ x _{1} x_{2} = c$

${x}^{2} - 7x + 11 = 0 \\ x_{1} + x_{2} =7 \\ x_{1} x_{2} = 11$

Ответ: сумма 7 ; произведение 11

${x}^{2} - 7x + 11 = 0 \\ a = 1\\ b = - 7 \\ c =11 \\ D = {b}^{2} - 4ac = ( - 7) {}^{2} - 4 \times 1 \times 11 = \\ = 49 - 44 = 5 \\ x_{1} = \frac{7 + \sqrt{5} }{2} \\ x_{2} = \frac{7 - \sqrt{5} }{2}$