Question

simplify
if 5+root6/5-root6 = a+3rootb

Answer 1

ʜᴇy ᴜꜱᴇʀ

ʜᴇʀᴇ ɪꜱ yᴏᴜʀ ᴀɴꜱᴡᴇʀ ;-

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$\frac{5 + \sqrt{6} }{5 - \sqrt{6} } = a + 3 \sqrt{b} \\ \\ \frac{(5 + \sqrt{6})(5 + \sqrt{6} ) }{(5 + \sqrt{6})(5 - \sqrt{6}) } = a + 3 \sqrt{b} \\ \\ \frac{ {(5 + \sqrt{6}) }^{2} }{ {5}^{2} - { \sqrt{6} }^{2} } = a + 3 \sqrt{b} \\ \\ \frac{25 + 6 + 10 \sqrt{6} }{25 - 6} = a + 3 \sqrt{b} \\ \\ \frac{31 + 10 \sqrt{6} }{19} = a + 3 \sqrt{b} \\ \\ a \: = \frac{31}{19} \\ \\ 3 \sqrt{b} = \frac{10 \sqrt{6} }{19 } \\ \\ \sqrt{b} = \frac{10 \sqrt{6} }{57}$