least value of f(x,y)

Level pending

If \(f(x,y) = \sqrt{x^2+y^2} + \sqrt{(x-1)^2 + y^2} +\sqrt{x^2+(y-1)^2} + \sqrt{(x-3)^2+(y-4)^2}\).

If least value of \(f(x,y) = a+b\sqrt{c}\), where \(a,b,c\) are positive integers and \(x,y\in \mathbb{R}\). Then \(a+b+c = \)

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