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in Sets, relations and functions by (20 points)
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Let \( f(x)=\sqrt{x-2}+\sqrt{x+47-14 \sqrt{x-2}} \) be a real valued function for \( x \geq 2 \), then the value of \( f(50)+f(66) \) is equal to

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f(x) = \(\sqrt{x-2}\) + \(\sqrt{x+47-14\sqrt{x-2}}\) ; x \(\geq\) 2

∴ f(50) = \(\sqrt{48}\) + \(\sqrt{50+47-14\times4\sqrt3}\)

 = 4\(\sqrt3+\sqrt{97-56\sqrt3}\)

f(66) = \(\sqrt{64}+\sqrt{66+47-14\sqrt{64}}\)

 = 8 + \(\sqrt{113-112}\)

 = 8 + 1

 = 9

∴ f(50) + f(66) = 4\(\sqrt3+\sqrt{97-56\sqrt3}+9\)

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