Where did the $$2$$ come from?

Algebra Level 5

$\large K\sqrt{N}\le (a+2b^{2}+2c^{2})$

The above inequality holds for all positive real numbers $$a,b,c$$. Here $$K$$ is a constant and $$N=abc$$.

When equality occurs,let the value of $$\dfrac{a}{b^{2}}=x$$

Find $$K^{x}$$.

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