Question

if 3+Г7÷3-Г7=a+bГ7find the value of a and b

Answer 1

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } = a + b \sqrt{7}$

By Rationalization,

$\frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } = a + b \sqrt{7} \\ \\ \\ \frac{(3 + \sqrt{7}) ^{2} }{ {(3)}^{2} - {( \sqrt{7}) }^{2} } = a + b \sqrt{7} \\ \\ \\ \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} = a + b \sqrt{7} \\ \\ \\ \frac{16 + 6 \sqrt{7} }{2} = a + b \sqrt{7} \\ \\ \frac{2(8 + 3 \sqrt{7} )}{2} = a + b \sqrt{7} \\ \\ 8 + 3 \sqrt{7} = a + b \sqrt{7}$


Comparing values, we get

a = 8
b = 3




I hope this will help you

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