Question

prove that 1/2√3 + 2/√5√3 + 1/2-√5=0​

Answer 1

Answer:

YOUR ANSWER IS ATTACHED IN PICTURE

Answer 2

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies \frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} } = 0 \\ \\ \red{\underline \bold{To \: Prove:}} \\ \tt: \implies \frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} } = 0$

• According to given question :

$\tt \circ \:\:\frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} } = 0\\ \\ \bold{Solving \: L.H.S} \\ \tt: \implies \frac{1}{2 + \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } + \frac{1}{2 - \sqrt{5} } \\ \\ \tt: \implies \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } + \frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } + \frac{1}{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } \\ \\ \tt: \implies \frac{2 - \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } + \frac{ 2\sqrt{5} + 2 \sqrt{3} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3}) }^{2} } + \frac{2 + \sqrt{5} }{ {2}^{2} - {( \sqrt{5}) }^{2} } \\ \\ \tt: \implies \frac{2 - \sqrt{3} }{4 - 3} + \frac{2 \sqrt{5} + 2\sqrt{3} }{5 - 3} + \frac{2 + \sqrt{5} }{4 - 5} \\ \\ \tt: \implies 2 - \sqrt{3} + \sqrt{5} + \sqrt{3} - 2 - \sqrt{5} \\ \\ \green{\tt: \implies 0} \\ \\ \green{\tt\:L.H.S=R.H.S} \\\\\huge{\red {\bold{Proved }}}$