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Let a and b be the solutions to\( 5x^2 - 11x + 4 = 0.\)  Find\( \[\frac{1}{a} + \frac{1}{b}.\]\)
 

 Feb 26, 2021
 #1
avatar+32 
0

We can solve this problem using Vieta's theorem. We want to find $\frac{1}{a} + \frac{1}{b}$, which simplifies to $\frac{b+a}{ab}$. Using Vieta's, we know that $a+b = -\frac{b}{a}$ and $ab = \frac{c}{a}$, where $a,b,c$ refer to a quadratic $ax^2+bx+c.$ Therefore, $a=5, b=-11, c=4. $ Using this, we find that $a+b = \frac{11}{5}$, and $ab = \frac{4}{5}$. Thus, we can find that $\frac{1}{a} + \frac{1}{b} = \boxed{\frac{11}{4}}.$

 Feb 26, 2021
 #2
avatar+34315 
+1

Use quadratic formula   a = 5     b= -11      c = 4

 

to find   x      11/10 +- sqrt 41 /10

 

1/a  + 1/b     =     10 /(11 + sqrt41)  + 10 / (11-sqrt41)

                   =    (110 + 110 )/( 121-41)

                    = 220 / 80

                    = 11/4                         Just as BB found !

 

 

then 1b + 1/ a = 2.75

 Feb 26, 2021
edited by ElectricPavlov  Feb 26, 2021
edited by ElectricPavlov  Feb 26, 2021

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