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A=3+52+3+5+3−52−3−5A=\dfrac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\dfrac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}A=2+3+53+5+2−3−53−5
If AAA can be expressed as a+bca+b\sqrt{c}a+bc for non-negative integers a,b,ca,b,ca,b,c with ccc square free, then find the value of a+b+ca+b+ca+b+c.
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