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[Solved] Numbers

 
Quadratic Equations
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June 15, 2021 10:28 am
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(@armor)
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If  a<b<0  and  a^2+b^2=4ab,   evaluate   \frac{a+b}{a-b}.

 

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June 15, 2021 10:28 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small a^2+b^2=4ab\Rightarrow (a+b)^2=6ab.  Since  \small a<b<0,    \small a+b=-\sqrt{6ab}.

Similarly, we can obtain \small a-b=-\sqrt{2ab}.  Hence

\small \frac{a+b}{a-b}=\frac{-\sqrt{6ab}}{-\sqrt{2ab}}=\sqrt{3}.

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