Question

$( \sqrt{5 } + 1 + \sqrt{5)} ^{2}$
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Answer 1

$( \sqrt{5 } + 1 + \sqrt{5)} ^{2}$

${(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2xz$

Here,

$x = \sqrt{5} ,y = 1,z = \sqrt{5}$

$= { (\sqrt{5} )}^{2} + {1}^{2} + (\sqrt{5} ){}^{2} + 2( \sqrt{5})(1) + 2(1)( \sqrt{5}) + 2( \sqrt{5} )( \sqrt{5} ) \\ = 5 + 1 + 5 + 2 \sqrt{5} + 2 \sqrt{5} + 2(5) \\ = 5 + 1 + 5 + 4(5) + 10 \\ = 41$

Hope this will be helpful.