If $$\sqrt 2 $$ : $$\left( {1 + \sqrt 3 } \right)$$ :: $$\sqrt 6 $$ : $$x$$, then $$x$$ is equal to –
a) $$\sqrt 3 + 3$$
b) $$1 – \sqrt 3 $$
c) $$1 + \sqrt 3 $$
d) $$\sqrt 3 – 3$$
Answer: a
Explanation:
$$\eqalign{
& = \sqrt 2 :\left( {1 + \sqrt 3 } \right)::\sqrt 6 😡 \cr
& \sqrt {2}x = \sqrt 6 \left( {1 + \sqrt 3 } \right) \cr
& x = \frac{{\sqrt 6 \left( {1 + \sqrt 3 } \right)}}{{\sqrt 2 }} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 \left( {1 + \sqrt 3 } \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt 3 + 3 \cr} $$
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