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# Algebra

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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
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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

Apr 28, 2022
#2
+2440
+1

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