Minimum of Squares!

Algebra Level 3

If \( \color{darkblue}a + \color{darkgreen}b = \color{magenta}{1} \quad and \quad \color{darkblue}a , \color{darkgreen}b > \color{brown}0 \)
Then \(\text{minimum value}\) of :

\[ \left( \color{darkblue}a \color{orange}+ \dfrac{\color{magenta}1}{\color{darkblue}a} \right)^{\color{red}2 }\color{blue}+ \left( \color{darkgreen}b \color{orange}+ \dfrac{\color{magenta}1}{\color{darkgreen}b} \right)^{\color{red}2} \geq \ ?\]

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