Question

Find this. ASAP...........!​

Answer 1

Question:-

• Solve the following.

Working out:-

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

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

$\sf \implies \frac{{(2 + \sqrt{3} )}^{2} }{ {2}^{2} - {\sqrt{3}}^{2} } = a + b \sqrt{3}$

$\sf \implies \frac{ {(2)}^{2} + {( \sqrt{3}) }^{2} + 2 \times 2 \times \sqrt{3} } {4 - 3} = a + b \sqrt{3}$

$\sf \implies \frac{ 5 + 4\sqrt{3} } {1} = a + b \sqrt{3}$

$\sf \implies 5 + 4 \sqrt{3} = a + b \sqrt{3}$

Comparing both side, we get,

$\sf a = 5 \: and \: b = 4$

Answer:-

• $\sf a = 5$
• $\sf b = 4$