Question

Вычислите: sqrt (8-2sqrt(7)) - sqrt(8+2sqrt(7))

Answer 1

Объяснение:

$\sqrt{8-2\sqrt{7} }-\sqrt{8+\sqrt{7} } =\sqrt{7+1-2\sqrt{7} } -\sqrt{7+1+2\sqrt{7} } =\\=\sqrt{(\sqrt{7})^2 -2*\sqrt{7}*1+1^2 } -\sqrt{(\sqrt{7})^2 +2*\sqrt{7}*1+1^2 } =\\=\sqrt{(\sqrt{7}-1)^2 } -\sqrt{(\sqrt{7}+1)^2 }=|\sqrt{7} -1|-|\sqrt{7} +1|=\sqrt{7}-1-\sqrt{7}-1=-2.$