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Algebra Level 4

What is the smallest value (round off to 1 decimal point) that

49+a272a+a2+b22ab+50+b210b\sqrt{49+a^2-7\sqrt2a}+\sqrt{a^2+b^2-\sqrt2ab}+\sqrt{50+b^2-10b}

can have for positive real numbers aa and bb?

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