Question

radical din (24-x^2) - radical din (8-x^2)=2 atunci radical din (24-x^2) + radical din (8-x^2) = ?

Answer 1

[tex](a-b)(a+b)=a^2-b^2\\ \sqrt{24-x^2}-\sqrt{8-x^2}=2\\ (\sqrt{24-x^2}-\sqrt{8-x^2})(\sqrt{24-x^2}+\sqrt{8-x^2})=\\ =(\sqrt{24-x^2})^2-(\sqrt{8-x^2})^2=24-x^2-8+x^2=16\\ 2(\sqrt{24-x^2}+\sqrt{8-x^2})=16\Leftrightarrow\sqrt{24-x^2}+\sqrt{8-x^2}=8[/tex]