The sum of the inverses of the solutions of the quadratic equation is equal to 2.75.
How to find the solutions of the quadratic equation?
Here we the quadratic equation:
0 = 5x^2 - 11x + 4
The solutions are given by Bhaskara's formula:
[tex]x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*5} }{2*5} \\\\x = \frac{11 \pm \sqrt{41} }{10}\\\\[/tex]
So the two solutions are:
[tex]a = \frac{11 + \sqrt{41} }{10}\\\\\\b = \frac{11 - \sqrt{41} }{10}[/tex]
Then we have:
[tex]\frac{1}{a} + \frac{1}{b} = \frac{10}{11 + \sqrt{41} } + \frac{10}{11 - \sqrt{41} } \\\\= \frac{10*(11 + \sqrt{41} + 11 - \sqrt{41}) }{(11 + \sqrt{41})*(11 - \sqrt{41})} \\\\= \frac{10*(11 + 11 ) }{(11 + \sqrt{41})*(11 - \sqrt{41})}\\\\= \frac{220}{80} = 2.75[/tex]
If you want to learn more about parabolas:
https://brainly.com/question/4061870
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