+42 Let a and b be the solutions to 5x^2 - 11 + 4 = 0. Find 1/a + 1/b
+344 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.
+2668 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 \({1 \over a} + {1 \over b} = {{11 \over 5} \over {4 \over 5}} = \color{brown}\boxed{11 \over 4}\)
