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

 Jun 3, 2022
 #1
avatar+280 
0

Hi I am sorry, did you mean 5x^2 - 11x + 4 = 0? If yes, then 1/a + 1/b = 0

If not, then there's only 1 answer.

 Jun 3, 2022
 #2
avatar+42 
0

Ah, apologies, yes, it should be 11x! Thanks :))

Celestianee  Jun 3, 2022
edited by Celestianee  Jun 3, 2022
 #3
avatar+42 
0

but it's wrong so- 😅😅

Celestianee  Jun 3, 2022
 #4
avatar+280 
0

are you sure it's wrong? I thought fractions that were negative and positive and have the same numbers cancel, and I even checked with a calculator. But I guess it's wrong

hipie  Jun 3, 2022
 #5
avatar+280 
0

Oh wait, I was computing 5x^2 - 11 + 4 = 0, not 5x^2 - 11x + 4, lol, oh well, the answer is really 11/4

hipie  Jun 3, 2022
 #6
avatar+1829 
+1

Note that \({ 1 \over a} + {1 \over b} = {a \over ab} + {b \over ab} ={ {a + b} \over ab}\)

 

Now, we can use Vieta's formula (\({-b \over a} = {11 \over 5}\)) to find a+b.

 

We can also use \({c \over a} = {4 \over 5}\) to find ab.

 

This means \({1 \over a} + {1 \over b} = {{11 \over 5} \over {4 \over 5}} = \color{brown}\boxed{11 \over 4}\)

 Jun 4, 2022

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