Question

(2+√3)³/²+(2-√3)³/² = ?

Answer 1

${(2 + \sqrt{3} })^{3 \div 2 + 3 \div 2}$
=
${(2 + \sqrt{3} )}^{3}$

Answer 2

Hope u like my process
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Formula to be used
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=> x³ +y³ = (x+y) (x²- xy + y²)
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$= > {(2 + \sqrt{3}) }^{ \frac{3}{2} } + {(2 - \sqrt{3}) }^{ \frac{3}{2} } \\ \\ = {( \sqrt{2 + \sqrt{3} } )}^{3} + {( \sqrt{2 - \sqrt{3} } )}^{3} \\ \\ = ( \sqrt{2 + \sqrt{3 } }+ \sqrt{2 - \sqrt{3} } )( {( \sqrt{2 + \sqrt{3} } )}^{2} - \sqrt{2 + \sqrt{3} } \sqrt{2 - \sqrt{3} } + {( \sqrt{2 - \sqrt{3} } )}^{2} ) \\ \\ = ( \sqrt{2 + \sqrt{3} } + \sqrt{2 - \sqrt{3} } )(2 + \sqrt{3 } - ( {2}^{2} - {( \sqrt{3} )}^{2} ) + 2 - \sqrt{3} ) \\ \\ = ( \sqrt{2 + \sqrt{3} } + \sqrt{2 - \sqrt{3} } )(4 - (4 - 3)) \\ \\ = ( \sqrt{2 + \sqrt{3} } + \sqrt{2 - \sqrt{3} } )(4 - 1) \\ \\ = \bf \: 3 (\sqrt{2 + \sqrt{3} } + \sqrt{2 - \sqrt{3} } )$
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Hope this is ur required answer

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