[tex]x = {(\sqrt{7} - 5 \sqrt{3} )}^{2} [/tex]
[tex]x = ({\sqrt{7})}^{2} - 2 \times \sqrt{7} \times 5 \sqrt{3} + {(5 \sqrt{3}) }^{2} [/tex]
[tex]x = 7 - 10 \sqrt{21} + 75[/tex]
[tex]x = 82 - 10 \sqrt{21} [/tex]
[tex]y = {(\sqrt{7} + 5 \sqrt{3}) }^{2} [/tex]
[tex]y = ({\sqrt{7})}^{2} + 2 \times \sqrt{7} \times 5 \sqrt{3} + {(5 \sqrt{3} )}^{2} [/tex]
[tex]y = 7+ 10 \sqrt{21} + 75[/tex]
[tex]y = 82 + 10 \sqrt{21} [/tex]
[tex]m_{h} = \frac{2}{ \frac{1}{x} + \frac{1}{y} } [/tex]
[tex]m_{h} = \frac{2}{ \frac{1}{82 - 10 \sqrt{21} } + \frac{1}{82 + 10 \sqrt{21} } } [/tex]
[tex]m_{h} = \frac{2}{ \frac{82 + 10 \sqrt{21} }{(82 - 10 \sqrt{21} )(82+ 10 \sqrt{21} )} + \frac{82 - 10 \sqrt{21} }{(82 - 10 \sqrt{21})(82 + 10 \sqrt{21} )} } [/tex]
[tex]m_{h} = \frac{2}{ \frac{82 + 10 \sqrt{21} + 82 - 10 \sqrt{21} }{(82 - 10 \sqrt{21})(82 + 10 \sqrt{21} ) } } [/tex]
[tex]m_{h} = \frac{2}{ \frac{164}{ {82}^{2} - {(10 \sqrt{21} )}^{2} } } [/tex]
[tex]m_{h} = \frac{2}{ \frac{164}{6724 - 2100} } [/tex]
[tex]m_{h} =\frac{2}{ \frac{164}{4624} } [/tex]
[tex]m_{h} = 2 \times \frac{4624}{164} [/tex]
[tex]m_{h} = \frac{4624}{82} [/tex]
[tex]m_{h} = \frac{2312}{41} [/tex]
