Question

$\sqrt{2} + \sqrt{3} \div 3 \sqrt{2} - 2 \sqrt{3} = a - b \sqrt{3}$
find A and B​

Answer 1

Answer:

We have,

$\large{ \sqrt{2} + \sqrt{3} \div 3 \sqrt{2} - 2 \sqrt{3} = a - b \sqrt{3} }$

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

$\large{ \implies \sqrt{2} + \frac{ \sqrt{3} }{ \sqrt{3} \times \sqrt{3} \times \sqrt{2} } - 2 \sqrt{3} = a - b \sqrt{3} }$

$\large{ \implies \sqrt{2} + \frac{ \cancel{ \sqrt{3} } }{ \cancel{ \sqrt{3} } \times \sqrt{3} \times \sqrt{2} } - 2 \sqrt{3} = a - b \sqrt{3} }$

$\large{ \implies \sqrt{2} + \frac{1}{ \sqrt{3} \times \sqrt{2} } - 2 \sqrt{3} = a - b \sqrt{3} }$

$\large{ \implies \sqrt{2} + \frac{1}{ \sqrt{6} } - 2 \sqrt{3} = a - b \sqrt{3} }$

On comparing both the sides, we get :

• $\Large{a = \sqrt{2} + \frac{1}{ \sqrt{6} } }$

• $\Large{b = 2}$

Step-by-step explanation:

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