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If (a + b)/(a - b) + (a - b)/(a + b) = 17/4, then what is a/b?

 Dec 4, 2021
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If (a + b)/(a - b) + (a - b)/(a + b) = 17/4, then what is a/b?

 

Hello Guest!

 

   x          y

\(\frac{a+b}{a-b}+\frac{a-b}{a+b}=\frac{17}{4}\)

  y          x

\(\frac{x}{y}+\frac{y}{x}=\frac{17}{4}\\ \frac{x^2+y^2}{xy}=\frac{17}{4}\\ y=\pm \sqrt{17-x^2}\\ y=\frac{4}{x}\)

grafisch gelöst:

x| -4   -1    1    4

y| -1   -4    4    1  

\(a+b=-4\\ \underline{a-b=-1}\\ 2a=-5\\ \color{blue}a=-2.5\\ \color{blue}b=1.5\)

 

\(a+b=-1\\ \underline{a-b=-4}\\ 2a=-5\\ \color{blue}a=-2.5\\ \color{blue}b=1.5\)

 

\(a+b=1\\ \underline{a-b=4}\\ 2a=5\\ \color{blue}a=2.5\\ \color{blue}b=-1.5\)

 

\(a+b=4\\ \underline{a-b=1}\\ 2a=5\\ \color{blue}a=2.5\\ \color{blue}b=1.5\)

 

\(\dfrac{a}{b}\in \{-\dfrac{5}{3},\dfrac{5}{3}\}\)

laugh  !

 Dec 4, 2021
edited by asinus  Dec 4, 2021

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