Question

Find the value of a (3 - sqrt(5))/(3 + 2sqrt(5)) = a * sqrt(5) - 19/11​

Answer 1

SOLUTION

TO DETERMINE

The value of a when

$\displaystyle\sf{ \frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } = \frac{a \sqrt{5} - 19}{11} }$

EVALUATION

Here it is given that

$\displaystyle\sf{ \frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } = \frac{a \sqrt{5} - 19}{11} }$

We now simplify it as below

$\displaystyle\sf{ \frac{3 - \sqrt{5} }{3 + 2 \sqrt{5} } = \frac{a \sqrt{5} - 19}{11} }$

$\displaystyle\sf{ \implies \: \frac{(3 - \sqrt{5} )(3 - 2 \sqrt{5})}{(3 + 2 \sqrt{5} )(3 - 2 \sqrt{5})} = \frac{a \sqrt{5} - 19}{11} }$

$\displaystyle\sf{ \implies \: \frac{9 - 6 \sqrt{5} - 3 \sqrt{5} + 10 }{(9 - 20)} = \frac{a \sqrt{5} - 19}{11} }$

$\displaystyle\sf{ \implies \: \frac{19 - 9 \sqrt{5} }{ - 11} = \frac{a \sqrt{5} - 19}{11} }$

$\displaystyle\sf{ \implies \: \frac{9 \sqrt{5} - 19 }{ 11} = \frac{a \sqrt{5} - 19}{11} }$

Comparing both sides we get a = 9

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Answer 2

Step-by-step explanation:

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