Question

find the values of a and b in 3-root5/3+2root5=aroot5-b/11

Answer 1

I hope this helps you.

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Answer 2

Answer:

a = 9 and b = 19

Step-by-step explanation:

Given that :

$\frac{3-\sqrt 5}{3+2\sqrt 5}=\frac{a\sqrt 5-b}{11}$

Now, Taking L.H.S. first and the rationalizing the denominator we get :

$\implies \frac{3-\sqrt 5}{3+2\sqrt 5}\\\\\implies \frac{3-\sqrt 5}{3+2\sqrt 5}\times \frac{3-2\sqrt 5}{3-2\sqrt 5}\\\\\implies \frac{9-6\sqrt 5-3\sqrt 5+2\times 5}{9-20}\\\\ \implies \frac{19-9\sqrt{5}}{-11}\\\\\implies \frac{9\sqrt 5-19}{11}\\\\\implies \frac{9\sqrt 5}{11}-\frac{19}{11}$

Now, Comparing the above expression with the R.H.S. We get ,

a = 9 and b = 19