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let a and b be the solutions to 5x^2-11x+4=0

find 1/a+1/b

 Dec 13, 2021
 #1
avatar+868 
+2

note 1/a + 1/b = (a+b)/ab

a+b = 11/5

ab = 4/5

(11/5)/(4/5) = 11/4

 Dec 13, 2021
 #2
avatar+13712 
+2

Find 1/a+1/b

 

Hello Guest!

 

\(5x^2-11x+4=0\\ x\in \{a,b\}=\{\frac{11}{10}+\frac{\sqrt{41}}{10},\frac{11}{10}-\frac{\sqrt{41}}{10}\}\)

\(\frac{1}{a}+\frac{1}{b}\\ \ =\frac{10}{11+\sqrt{41} }+\frac{10}{11-\sqrt{41} }\\ \ =\frac{110-10\cdot \sqrt{41}+110+10\cdot \sqrt{41} }{121-41}\\ \ =\frac{220}{80}\)

 

\(\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{11}{4}\)

laugh  !

 Dec 13, 2021

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