Question

Квадратные корни, полное решение!

Answer 1

Б1)
${ \sqrt{7 - 2 \sqrt{6} } - \sqrt{7 + 2 \sqrt{6} }) }^{2} = 7 - 2 \sqrt{6} - 2 \sqrt{7 - 2 \sqrt{6} } \sqrt{7 + 2 \sqrt{6} } + 7 + 2 \sqrt{6} = 14 - 2 \sqrt{ {7}^{2} - {(2 \sqrt{6}) }^{2} } = 14 - 2 \sqrt{49 - 24} = 14 - 2 \sqrt{25} = 14 - 2 \times 5 = 14 - 10 = 4$
Б2)
$\frac{1}{3 \sqrt{7} - 7} - \frac{1}{7 + 3 \sqrt{7} } = \frac{3 \sqrt{7} + 7 - (3 \sqrt{7} - 7) }{(3 \sqrt{7} - 7)(3 \sqrt{7} + 7) } = \frac{3 \sqrt{7} + 7 - 3 \sqrt{7} + 7}{ {(3 \sqrt{7}) }^{2} - {7}^{2} } = \frac{14}{63 - 49} = \frac{14}{14} = 1$