Question

(5-\(\dfrac{7-\sqrt{7}}{1-\sqrt{7}}\))(\(\dfrac{\sqrt{14}+\sqrt{7}}{1+\sqrt{2}}\)-5)

Answer 1

\(\left(5-\dfrac{7-\sqrt{7}}{1-\sqrt{7}}\right)\left(\dfrac{\sqrt{14}+\sqrt{7}}{1+\sqrt{2}}-5\right)\\ =\left(5-\dfrac{\sqrt{7}\left(\sqrt{7}-1\right)}{1-\sqrt{7}}\right)\left(\dfrac{\sqrt{7}\left(\sqrt{2}+1\right)}{1+\sqrt{2}}-5\right)\\ =\left(5+\dfrac{\sqrt{7}\left(\sqrt{7}-1\right)}{\sqrt{7}-1}\right)\left(\sqrt{7}-5\right)\\ =\left(5+\sqrt{7}\right)\left(\sqrt{7}-5\right)\\ =\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)\\ =\left(\sqrt{7}\right)^2-5^2\\ =7-25\\ =-18\)

 

Answer 2

\(\left(5-\dfrac{7-\sqrt{7}}{1-\sqrt{7}}\right)\left(\dfrac{\sqrt{14}+\sqrt{7}}{1+\sqrt{2}}-5\right)\)

\(=\left(5+\dfrac{\sqrt{7}-7}{1-\sqrt{7}}\right)\left(\dfrac{\sqrt{14}+\sqrt{7}}{1+\sqrt{2}}-5\right)\)

\(=\left[5+\dfrac{\sqrt{7}\left(1-\sqrt{7}\right)}{1-\sqrt{7}}\right]\left[\dfrac{\sqrt{7}\left(1+\sqrt{2}\right)}{1+\sqrt{2}}-5\right]\)

\(=\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)\)

\(=\left(\sqrt{7}\right)^2-5^2\)

\(=7-25\)

\(=-18\)