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

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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