Question

find the value of a and b

$\orange{ \bigstar}{\underline{\boxed{\mathsf{\frac{ \sqrt{11 - 3} }{ \sqrt{11 + 2} } = a - b \sqrt{11} }}}} \pink{\bigstar}$
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Answer 1

Hi Mate ! Here is your Answerrr!

Given:

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

To Find :

The value of a and b from the given equation

Process :

We will first try to rationalise the denominator of the given irrational number and make it in the format of RHS , we can then easily spot out the values of a and b

Solution:

We will first simply the equation and then Find its RF .

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

$\tt{ \implies a - b \sqrt{11} = \frac{ \sqrt{8} }{ \sqrt{13} } }$

$\tt{ \implies a - b \sqrt{11} = \frac{ \sqrt{8} }{ \sqrt{1 3} } \times \frac{ \sqrt{13} }{ \sqrt{13} } }$

$\tt{ \implies a - b \sqrt{11} = \frac{ \sqrt{8} \times \sqrt{13} }{13}}$

$\tt{ \implies a - b \sqrt{11} = \frac{ \sqrt{104} }{13} }$

Hence, we get from the situation that :

$\tt{\bull a= \frac{\sqrt{104}}{13}}$

• b = 0

Note : I think that you had done some mistake in question, if you have done, then you can upload another question and if possible I can solve it :)

Have A great Learning !

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