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`#tnvt`
`A=\sqrt{7-\sqrt{13}}-\sqrt{7+\sqrt{13}}+\sqrt{2}`
`=\frac{\sqrt{2}.(\sqrt{7-\sqrt{13}}-\sqrt{7+\sqrt{13}}+\sqrt{2})}{\sqrt{2}}`
`=\frac{\sqrt{14-2\sqrt{13}}-\sqrt{14+2\sqrt{13}}+2}{\sqrt{2}}`
`=\frac{\sqrt{\sqrt{13}^2-2.\sqrt{13}.1+1^2}-\sqrt{\sqrt{13}^2+2.\sqrt{13}.1+1^2}+2}{\sqrt{2}}`
`=\frac{\sqrt{(\sqrt{13}-1)^2}-\sqrt{(\sqrt{13}+1)^2}+2}{\sqrt{2}}`
`=\frac{|\sqrt{13}-1|-|\sqrt{13}+1|+2}{\sqrt{2}}`
`=\frac{\sqrt{13}-1-\sqrt{13}-1+2}{\sqrt{2}}`
`=\frac{0}{\sqrt{2}}`
`=0`
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