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[Solved] Equations

 
Quadratic Equations
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June 15, 2021 11:27 am
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(@armor)
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2(\frac{1}{x}-1)^2+5(\frac{1}{x}-1)=3\Rightarrow SS=?

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June 15, 2021 11:27 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small \frac{1}{x}-1=t

\small 2t^2+5t=3\Rightarrow 2t^2+5t-3=0\Rightarrow t=\frac{1}{2}, t=-3.

\small \frac{1}{x}-1=t

\small 1) t=\frac{1}{2}

\small \frac{1}{x}-1=\frac{1}{2}\Rightarrow \frac{1}{x}=\frac{3}{2}\Rightarrow x=\frac{2}{3}.

\small 2) t=-3

\small \frac{1}{x}-1=-3\Rightarrow \frac{1}{x}=-2\Rightarrow x=-\frac{1}{2}.

Therefore, \small SS=\left \{ -\frac{1}{2},\frac{2}{3} \right \}.

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