Question

a44 решите пожалуйста

Answer 1

$\sqrt{22 - \sqrt{160} } ( \sqrt{10} + 1) = \\ = \sqrt{22 - 4 \sqrt{10} } ( \sqrt{10} + 1) = \\ = \sqrt{2(11 - 2 \sqrt{10} )} ( \sqrt{10} + 1) = \\ = \sqrt{2} \cdot \sqrt{( ({ \sqrt{10}) }^{2} - 2 \sqrt{10} + 1) } ( \sqrt{10} + 1) = \\ = \sqrt{2} \cdot \sqrt{( \sqrt{10} - 1) ^{2} } ( \sqrt{10} + 1) = \\ = \sqrt{2} \cdot | \sqrt{10} - 1 | ( \sqrt{10} + 1) = \\ = \sqrt{2} \cdot ( \sqrt{10} - 1 ) ( \sqrt{10} + 1) = \\ = ( {( \sqrt{10} )}^{2} - {1}^{2}) \sqrt{2} = \\ = (10 - 1) \sqrt{2} = 9 \sqrt{2}$