Question

2*root6+root5/3*root5+2*root6=p+root30 q find p and q

Answer 1

$\textbf{Solution:}$

$\frac{2 \sqrt{6} + \sqrt{5} }{3 \sqrt{5} + 2 \sqrt{6} } = p + \sqrt{30} \: \: q \\ \\ \frac{2 \sqrt{6} + \sqrt{5} }{3 \sqrt{5} + 2 \sqrt{6} } \times \frac{3 \sqrt{5} - 2 \sqrt{6} }{3 \sqrt{5} - 2 \sqrt{6} } \\ \\ \frac{2 \sqrt{6} (3 \sqrt{5} - 2 \sqrt{6} ) + \sqrt{5} (3 \sqrt{5} - 2 \sqrt{6} ) }{(3 \sqrt{5}) {}^{2} - (2 \sqrt{6}) {}^{2} } \\ \\ \frac{6 \sqrt{30} - 24 + 15 - 2 \sqrt{30} }{45 - 24} \\ \\ \frac{4 \sqrt{30} - 9 }{21}$

Therefore,

You can conclude the value of P and Q.

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$\textbf{Thank you!!}$