Resposta:
x = -2
Explicação passo-a-passo:
[tex]x=\sqrt{3-\sqrt{8}}-\sqrt{3+\sqrt{8}}\\x=\sqrt{3-2\sqrt{2}}-\sqrt{3+2\sqrt{2}}\\x=\sqrt{2-2\sqrt{2}+1}-\sqrt{2+2\sqrt{2}+1}\\x=\sqrt{1\cdot \:2-2\sqrt{2}+1}-\sqrt{1\cdot \:2+2\sqrt{2}+1}\\x=\sqrt{\left(\sqrt{1}\right)^2\left(\sqrt{2}\right)^2-2\sqrt{2}+\left(\sqrt{1}\right)^2}-\sqrt{\left(\sqrt{1}\right)^2\left(\sqrt{2}\right)^2+2\sqrt{2}+\left(\sqrt{1}\right)^2}[/tex]
[tex]x=\sqrt{1^2\left(\sqrt{2}\right)^2-2\sqrt{2}+1^2}-\sqrt{1^2\left(\sqrt{2}\right)^2+2\sqrt{2}+1^2}\\x=\sqrt{\left(1\cdot \sqrt{2}-1\right)^2}-\sqrt{\left(1\cdot \sqrt{2}+1\right)^2}\\x=1\cdot \sqrt{2}-1-1\cdot \sqrt{2}+1\\x=\sqrt{2}-1-\sqrt{2}+1[/tex]
[tex]=\sqrt{2}-1-\left(1+\sqrt{2}\right)\\x=\sqrt{2}-1-\sqrt{2}-1\\x=\sqrt{2}-\sqrt{2}-2\\x=-2[/tex]
