Challenge Evaluate the sum

anemone

Paris la ville de l'amour
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Jan 28, 2018
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#1
Given that \(\displaystyle abx^2=(a-b)^2(x+1)\).

Find \(\displaystyle 1+\dfrac{4}{x}+\dfrac{4}{x^2}\).
 
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MarkFL

La Villa Strangiato
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#2
I would begin by writing:

\(\displaystyle 1+\frac{4}{x}+\frac{4}{x^2}=1+4\frac{x+1}{x^2}=1+4\frac{ab}{(a-b)^2}=\left(\frac{a+b}{a-b}\right)^2\)
 
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anemone

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#3
Bravo, Mark! (Cool)
 
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