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Question Number 99655 by bemath last updated on 22/Jun/20

Commented by bramlex last updated on 22/Jun/20

$$approximationx=7.464$$$$\iff x-2\sqrt{x}=7.464-2\sqrt{7.464}\approx 1.9999355...$$

Answered by Farruxjano last updated on 22/Jun/20

$$\mathit{l}\mathit{e}\mathit{t}\sqrt{\mathit{x}}=\mathit{y}:$$$${\mathit{y}}^4-16\mathit{y}=12\Rightarrow {\mathit{y}}^4+4{\mathit{y}}^2+4-4{\mathit{y}}^2-16\mathit{y}-16=0$$$${({\mathit{y}}^2+2)}^2-{(2\mathit{y}+4)}^2=0\Rightarrow ({\mathit{y}}^2-2\mathit{y}-2)({\mathit{y}}^2+2\mathit{y}+6)=0$$$$\mathit{c}\mathit{a}\mathit{s}\mathit{e}\left(1\right):{\mathit{y}}^2+2\mathit{y}+6=0\Rightarrow \mathit{D}<0\Rightarrow \mathit{\varnothing }$$$$\mathit{c}\mathit{a}\mathit{s}\mathit{e}\left(2\right):{\mathit{y}}^2-2\mathit{y}-2=0\Rightarrow \mathit{D}>0\Rightarrow$$$${\mathit{y}}^2-2\mathit{y}=2\Rightarrow \mathit{y}=\sqrt{\mathit{x}}\Rightarrow \mathit{x}-2\sqrt{\mathit{x}}=2\mathit{A}\mathit{n}\mathit{s}:2$$

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