Let a and b be the solutions to\( 5x^2 - 11x + 4 = 0.\) Find\( \[\frac{1}{a} + \frac{1}{b}.\]\)
+32 We can solve this problem using Vieta's theorem. We want to find $\frac{1}{a} + \frac{1}{b}$, which simplifies to $\frac{b+a}{ab}$. Using Vieta's, we know that $a+b = -\frac{b}{a}$ and $ab = \frac{c}{a}$, where $a,b,c$ refer to a quadratic $ax^2+bx+c.$ Therefore, $a=5, b=-11, c=4. $ Using this, we find that $a+b = \frac{11}{5}$, and $ab = \frac{4}{5}$. Thus, we can find that $\frac{1}{a} + \frac{1}{b} = \boxed{\frac{11}{4}}.$
+37146 Use quadratic formula a = 5 b= -11 c = 4
to find x 11/10 +- sqrt 41 /10
1/a + 1/b = 10 /(11 + sqrt41) + 10 / (11-sqrt41)
= (110 + 110 )/( 121-41)
= 220 / 80
= 11/4 Just as BB found !
then 1b + 1/ a = 2.75
