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\(\sqrt{52+4x}+\sqrt{52-4x}=12\)

Ermittle x.

 17.06.2021
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\(\sqrt{52+4x}+\sqrt{52-4x}=12 \ \ |^2 \\ 52+4x +2\cdot \sqrt{52+4x}\cdot \sqrt{52-4x} +52-4x = 12 \\ 52 +2\cdot \sqrt{52+4x}\cdot \sqrt{52-4x} +52 = 12 \\ 104 + 2\cdot \sqrt{52^2-(4x)^2} = 12 \ \ \ |-104 \\ 2\sqrt{2704-16x^2} = -92 \ \ |:2 \\ \sqrt{2704-16x^2} = -46 \ \ |^2 \\ 2704-16x^2 = 2116 \ \ |+16x^2 -2116 \\ 588 = 16x^2 \ \|:16 \\ 36,75 = x^2 \\ \Rightarrow x_{1/2} = \pm \sqrt{36,75}\)

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 17.06.2021

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