If 5-root6/5+root6=a-b root6 then find the value of a and b
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Answer:
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\begin{gathered}\frac{5 + \sqrt{6} }{5 - \sqrt{6} } = a + b \sqrt{6} \\ rationalize \\ \frac{5 + \sqrt{6} }{5 - \sqrt{6} } \times \frac{5 + \sqrt{6} }{5 + \sqrt{6} } = a + b \sqrt{6} \\ \frac{ {(5 + \sqrt{6}) }^{2} }{25 - 6} = a + b \sqrt{6} \\ \frac{25 + 6 + 10 \sqrt{6} }{19} = a + b \sqrt{6} \\ \frac{31 + 10 \sqrt{6} }{19} = a + b \sqrt{6} \\ \frac{31}{19} + \frac{10}{19} \sqrt{6} = a + b \sqrt{6} \\ a = \frac{31}{19} \: and \: b = \frac{10}{19}\end{gathered}
5−
6
5+
6
=a+b
6
rationalize
5−
6
5+
6
×
5+
6
5+
6
=a+b
6
25−6
(5+
6
)
2
=a+b
6
19
25+6+10
6
=a+b
6
19
31+10
6
=a+b
6
19
31
+
19
10
6
=a+b
6
a=
19
31
andb=
19
10
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