resolva as equação irracionais : a)√x+1=7 b)√√3x+1=2 c)√3+x=√9-x d)³√√3x+1=2 e)√2x-3-√x+11=0 f)√x-√x+2=0

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a) \(\sqrt {x + 1} = 7 \Leftrightarrow x + 1 = {7^2} \Leftrightarrow x + 1 = 49 \Leftrightarrow x = 49 - 1 \Leftrightarrow \boxed{x = 48}\)

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b) \(\sqrt {\sqrt {3x + 1} } = 2 \Leftrightarrow \sqrt {3x + 1} = {2^2} \Leftrightarrow \sqrt {3x + 1} = 4 \Leftrightarrow 3x + 1 = {4^2} \Leftrightarrow 3x + 1 = 16 \Leftrightarrow 3x = 16 - 1 \Leftrightarrow 3x = 15 \Leftrightarrow x = {{15} \over 3} \Leftrightarrow \boxed{x = 5}\)

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c) \(\sqrt {3 + x} = \sqrt {9 - x} \Leftrightarrow x + 3 = 9 - x \Leftrightarrow x + x = 9 - 3 \Leftrightarrow 2x = 6 \Leftrightarrow x = {6 \over 2} \Leftrightarrow \boxed{x = 3}\)

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d) \(\root 3 \of {\sqrt {3x + 1} } = 2 \Leftrightarrow \sqrt {3x + 1} = {2^3} \Leftrightarrow \sqrt {3x + 1} = 8 \Leftrightarrow 3x + 1 = {8^2} \Leftrightarrow 3x + 1 = 64 \Leftrightarrow 3x = 64 - 1 \Leftrightarrow 3x = 63 \Leftrightarrow x = {{63} \over 3} \Leftrightarrow \boxed{x = 21}\)

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e) \(\sqrt {2x - 3} - \sqrt {x + 11} = 0 \Leftrightarrow \sqrt {2x - 3} = \sqrt {x + 11} \Leftrightarrow 2x - 3 = x + 11 \Leftrightarrow 2x - x = 11 + 3 \Leftrightarrow \boxed{x = 14}\)

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f) \(\sqrt x - \sqrt {x + 2} = 0 \Leftrightarrow \sqrt x = \sqrt {x + 2} \Leftrightarrow x = x + 2 \Leftrightarrow x - x = 2 \Leftrightarrow 0x = 2 \Leftrightarrow x = {2 \over 0} \Leftrightarrow \boxed{x = \emptyset}\)