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Let a and b be the solutions to 5x^2-11x+4=0. Find 1/(a + b).

 Apr 28, 2022
 #1
avatar+9 
0

First solve the quadratic by using the quadratic formula, x = (-(-11)+/- sqrt((-11)^2-4(5)(4)))/2(5) ---> x = (11+/- sqrt(41))/10. 

 

sps. a = (11+sqrt(41))/10 and b = (11-sqrt(41))/10

then a+b just equals 22/10 = 11/5 

 

the question asks for the reciprocal therefore the answer is 5/11.

 Apr 28, 2022
 #2
avatar+1365 
+2

Using Vieta's, the sum of the roots \((a+b)\) is \({11 \over 5}\)

 

Plugging this in, we have: \(\large{1 \over {11 \over 5}} = \color{brown}\boxed{5 \over 11}\)

 Apr 29, 2022

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