Question

prove that:1/2+√3 + 2/✓5-√3 + 1/2-√5 =0​

Answer 1

Step-by-step explanation:

To Prove-

$( \frac{1}{2 + \sqrt{3} } ) + (\frac{2}{ \sqrt{5} - \sqrt{3} }) + ( \frac{1}{2 - \sqrt{5} } ) = 0$

ㅤ

Proof -

$( \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } ) + ( \frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } ) + ( \frac{1}{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } ) = 0 \\ \\ ( \frac{2 - \sqrt{3} }{(2 {)}^{2} - ( \sqrt{3} {)}^{2} } ) + ( \frac{2( \sqrt{5} + \sqrt{3}) }{( \sqrt{5 } {)}^{2} - ( \sqrt{3} {)}^{2} } ) + ( \frac{2 + \sqrt{5} }{(2 {)}^{2} - ( \sqrt{5} {)}^{2} } ) = 0 \\ \\ ( \frac{2 - \sqrt{3} }{4 - 3} ) + (\frac{2( \sqrt{5} + \sqrt{3} ) }{5 - 3} ) +( \frac{2 + \sqrt{5} }{4 - 5} = 0 \\ \\ 2 - \sqrt{3} + \sqrt{5} + \sqrt{3} - 2 + \sqrt{5} = 0 \\ \\ 0 = 0$

Hence proved.