Problem Solving (PS) | Re: If x-5=x+5 , x=?

Given: \(x-5 = \sqrt{x} + \sqrt{5}\)

=>\((\sqrt{x})^2 - (\sqrt{5})^2 = \sqrt{x} + \sqrt{5}\)
=> \((\sqrt{x} + \sqrt{5})(\sqrt{x} - \sqrt{5}) = \sqrt{x} + \sqrt{5}\)
=>\((\sqrt{x} - \sqrt{5}) = (\sqrt{x} + \sqrt{5}) / (\sqrt{x} + \sqrt{5})\)
=>\((\sqrt{x} - \sqrt{5}) = 1\) =>\(\sqrt{x} = \sqrt{5} + 1\)

Squaring both sides
=>\(x= 1+5 +2*1* \sqrt{5}\) =>\(x= 6+2\sqrt{5}\)
Answer: A
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