Question

Можно подробно, по действиям?

(3+$\sqrt{7}$)$^{2}$ + (3-$\sqrt{7}$)$^{2}$

Answer 1

Ответ:

$(3 + \sqrt{7} ) {}^{2} + (3 - \sqrt{7} ) {}^{2}$

$1) {(3 + \sqrt{7} )}^{2} = {3}^{2} + 2 \times 3 \times \sqrt{7} + ( \sqrt{7} ) {}^{2} = \\ = 9 + 6 \sqrt{7} + 7 = 16 + 6 \sqrt{7}$

$2)(3 - \sqrt{7} ) {}^{2} = {3}^{2} - 2 \times 3 \times \sqrt{7} + {( \sqrt{7} )}^{2} = \\ = 9 - 6 \sqrt{7} + 7 = 16 - 6 \sqrt{7}$

Получаем:

$(3 + \sqrt{7} ) {}^{2} + (3 - \sqrt{7} ) {}^{2} = \\ = 16 + 6 \sqrt{7} + 16 - 6 \sqrt{7} = 32$