Question

уравнение $\sqrt{11-6 \sqrt{2} } *x + \sqrt{11+6 \sqrt{2} } *x= -24$

Answer 1

$\sqrt{11 - 6\sqrt{2} } } \cdot x + \sqrt{11 +6 \sqrt{2} } } \cdot x = -24 \\ \\ x( \sqrt{9 - 6 \sqrt{2} + 2 } + \sqrt{9 - 6 \sqrt{2} + 2 } ) = -24 \\ \\ x(( \sqrt{(3 - \sqrt{2} })^2 + ( \sqrt{(3 + \sqrt{2} })^2 ) = -24 \\ \\ x(3 - \sqrt{2} + 3 + \sqrt{2}) = -24 \\ \\ 6x = -24 \\ \\ \boxed{x = -4}$

Answer 2

$\sqrt{11-6\sqrt{2}}x+\sqrt{11+6\sqrt{2}}x=-24\\x=-\cfrac{24}{\sqrt{11-6\sqrt{2}}+\sqrt{11+6\sqrt{2}}}=-\cfrac{24}{\sqrt{(3-\sqrt{2})^2}+\sqrt{(3+\sqrt{2})^2}}=\\-\cfrac{24}{|3-\sqrt{2}|+|3+\sqrt{2}|}=-\cfrac{24}{3-\sqrt{2}+3+\sqrt{2}}=-\frac{24}{6}=-4$