Question

2/4+root3 + 1/2+root3 = a+b root 3​

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

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$\sf{Given : \: \: \: \: \: \: \: \: \frac{2}{4} + \sqrt{3} + \frac{1}{2} + \sqrt{3} = a + b \sqrt{3}}$

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$\sf{→\frac{\cancel{2}}{\cancel{4}} + \sqrt{3} + \frac{1}{2} + \sqrt{3} = a + b\sqrt{3}} \\ \\ \sf{→\frac{1}{2} + \sqrt{3} + \frac{1}{2} + \sqrt{3} = a + b\sqrt{3}} \\ \\ \bf{Taking \: LCM} \\ \\ \sf{→\dfrac{1 + 2\sqrt{3} + 1 + 2\sqrt{3}}{2} = a + b\sqrt{3}} \\ \\ \sf{→\dfrac{\cancel{2}(1 + 2\sqrt{3})}{\cancel{2}} = a + b\sqrt{3}} \\ \\ \sf{→1 + 2\sqrt{3} = a + b\sqrt{3}}$

Hence, a = 1, b = 2