Răspuns:
[tex](a) \boldsymbol{ \red{-10\sqrt{2}}} , (b) \boldsymbol{ \red{\sqrt{3}}}[/tex]
Explicație pas cu pas:
Scoatem întregii de sub radical:
[tex]a) 2(x + \sqrt{18} ) = x - \sqrt{32}[/tex]
[tex]2(x + \sqrt{2 \cdot 3^2} ) = x - \sqrt{2 \cdot 4^2}[/tex]
[tex]2(x + 3\sqrt{2} ) = x - 4\sqrt{2}[/tex]
[tex]2x + 6\sqrt{2} = x - 4\sqrt{2}[/tex]
[tex]2x - x = - 4\sqrt{2} - 6\sqrt{2}[/tex]
[tex]x = - 10\sqrt{2}[/tex]
[tex]b) \sqrt{2}(x - \sqrt{3} ) = \sqrt{24} - x\sqrt{8}[/tex]
[tex]x\sqrt{2} - \sqrt{3 \cdot 2} = \sqrt{2^2 \cdot 6} - x\sqrt{2 \cdot 2^2}[/tex]
[tex]x\sqrt{2} + 2x\sqrt{2} = 2\sqrt{6} + \sqrt{6}[/tex]
[tex]3x\sqrt{2} = 3\sqrt{6}[/tex]
[tex]x = \dfrac{3\sqrt{6}}{3\sqrt{2}}^{(3} = \sqrt{\dfrac{6}{2} } = \sqrt{3}[/tex]
