Question

Можете найти значение выражения?

Answer 1

Ответ:

${x}^{2} + 2x - 7 = 0 \\ D = 4 + 28 = 32 \\ x1 = \frac{ - 2 + \sqrt{32} }{2} = \frac{ - 2 + \sqrt{16 \times 2} }{2} = \\ = \frac{ - 2 + 4 \sqrt{2} }{2} = - 1 + 2 \sqrt{2} \\ x2 = - 1 - 2 \sqrt{2}$

${x1}^{2} + {x2}^{2} = {(2 \sqrt{2} - 1)}^{2} + {( - 1 - 2 \sqrt{2}) }^{2} = \\ = 8 - 4 \sqrt{2} + 1 + 1 + 4 \sqrt{2} + 8 = \\ = 16 + 2 = 18$