Question

simplify 2 root 3 ( 3 + root 5 ) ( 1 - root 5 ) / 1 + root 5

Answer 1

 · 2 - √3 ---( 1 ) b ) 2 / ( √5 - √ 3 ) = 2 ( √5 + √3 ) / [ ( √5 - √3 )(√5 + √3 ) ] = 2( √5 + √3 ) / ( 5 - 3 ) = 2 ( √5 + √3 )/ 2

Answer 2

Answer :


$2 \sqrt{3} (3 + \sqrt{5} ) \times \frac{(1 - \sqrt{5} )}{1 + \sqrt{5} } \\ \\ multiply \: 2 \sqrt{3} \: by \: \frac{(1 - \sqrt{5} )}{1 + \sqrt{5} } \\ \\ \frac{2 \sqrt{3} \times (1 - \sqrt{5} ) }{1 + \sqrt{5} } \times (3 + \sqrt{5} ) \\ \\ multiply \: \\ \\ \frac{2 \sqrt{3}(1 - \sqrt{5} )(3 + \sqrt{5}) }{1 + \sqrt{5} } \\ \\ \frac{2 \sqrt{3} (1 - \sqrt{5} ) \times 3 + 2 \sqrt{3} (1 - \sqrt{5} ) \sqrt{5} }{1 + \sqrt{5} }$


$\frac{6 \sqrt{3} - 6 \sqrt{15} + 2 \sqrt{15} - 2 \sqrt{75} }{1 + \sqrt{5} } \\ \\ - 2 \sqrt{75} = - 10 \sqrt{3} \\ \\ \frac{6 \sqrt{3} - 6 \sqrt{15} + 2 \sqrt{15} - 10 \sqrt{3} }{1 + \sqrt{5} } \\ \\ collect \: the \: like \: terms \\ \\ we \: get \\ \\ \frac{6 \sqrt{3} - 10 \sqrt{3} - 6 \sqrt{15 } + 2 \sqrt{15} }{1 + \sqrt{5} } \\ \\ \frac{ - 4 \sqrt{3} - 4 \sqrt{15} }{1 + \sqrt{5} } \\ \\ - 4 \: and \: \sqrt{3} \: are \: common \: factor \\ \\ \frac{ - 4 \sqrt{3} ( 1+ \sqrt{5} )}{1 + \sqrt{5} } \\ \\ reduce \: (1 + \sqrt{5} ) \: from \: 1 + \sqrt{5} \\ \\ we \: get \: - 4 \sqrt{3}$


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