Liczba \( \left( 3 - \sqrt{2} \right)^2 + 4\left( 2 - \sqrt{2} \right) \) jest równa
| A. \( 19-10\sqrt{2} \) | B. \( 17-4\sqrt{2} \) | C. \( 15+14\sqrt{2} \) | D. \( 19+6\sqrt{2} \) |
\[ \class{color1}{\left( 3 - \sqrt{2} \right)^2} + \class{color2}{4\left( 2 - \sqrt{2} \right)}\class{mathHint hintWzorSkrocMnoz}{=} \class{color1}{3^2-2\cdot3\cdot\sqrt{2} + \sqrt{2}^2} + \class{color2}{4\cdot 2 - 4\sqrt{2}}=\\ =\class{color1}{9-6\cdot\sqrt{2}+2}+\class{color2}{8-4\sqrt{2}}=\class{color1}{11-6\cdot\sqrt{2}}+\class{color2}{8-4\sqrt{2}}=\\ =19-10\sqrt{2} \] Prawidłowa odpowiedź to A.