Aasav's square roots

1. Let $x^4+\frac{4}{x^4}=y$
2. $x^4+4+\frac{4}{x^4}=y+4$
3. $(x^2+\frac{2}{x^2})^2=y+4$
4. $((\sqrt { 2+\sqrt { 2 } } )^2+\frac{2}{(\sqrt { 2+\sqrt { 2 } } )^2})^2=y+4$
5. $(2+\sqrt{2}+\frac{2}{2+\sqrt{2} })^2=y+4$
6. $(2+\sqrt{2}+\frac{2}{2+\sqrt{2}}*\frac{2-\sqrt{2}}{2-\sqrt{2}})^2=y+4$
7. $(2+\sqrt{2}+\frac{2(2-\sqrt{2})}{2^2-(\sqrt{2})^2})^2=y+4$
8. $(2+\sqrt{2}+\frac{2(2-\sqrt{2})}{2})^2=y+4$
9. $(2+\sqrt{2}+2-\sqrt{2})^2=y+4$
10. $4^2=y+4$
11. $y=12$

Differentiate the function & get the max. value; Apply the periodicity of the values of X & then solve.

answer will be (X^2 + (2/X^2)) - 4 x^2=2+root2 1/x^2=2-root2 just manipualte and get 12