Вычеслите √(14 + 6 × √5) – √(9 – 4 × √5)

[latex]\sqrt{14+6\sqrt{5}}=\sqrt{9+6\sqrt{5}+5}=\\\\\sqrt{3^2+2*3*\sqrt{5}+(\sqrt{5})^2}=\\\\\sqrt{(3+\sqrt{5})^2=\\\\|3+\sqrt{5}|=3+\sqrt{5}[/latex] -------------- [latex]\sqrt{9-4\sqrt{5}}=\sqrt{4-4\sqrt{5}+5}=\\\\\sqrt{2^2-2*2*\sqrt{5}+(\sqrt{5})^2}=\\\\\sqrt{(2-\sqrt{5})^2}=\\\\|2-\sqrt{5}|=\sqrt{5}-2[/latex] так как [latex]2-\sqrt{5}=\sqrt{4}-\sqrt{5}<0[/latex] ----------------- [latex]\sqrt{14+6\sqrt{5}}-\sqrt{9-4\sqrt{5}}=(3+\sqrt{5})-(\sqrt{5}-2)=\\\\3+\sqrt{5}-\sqrt{5}+2=5[/latex] ответ: 5