\The two values of $x$ that satisfy the equation $35x^2 - 51x + 18 = 0$ can be written as simplified fractions $\dfrac{a}{b}$ and $\dfrac{c}{d}$, where $a$, $b$, $c$, and $d$ are all positive integers. What is the value of $ab + ad + bc + cd$?

michaelcai
Nov 14, 2017

#1**+1 **

I will take a crack at it !!

Solve for x:

35 x^2 - 51 x + 18 = 0

The left hand side factors into a product with two terms:

(5 x - 3) (7 x - 6) = 0

Split into two equations:

5 x - 3 = 0 or 7 x - 6 = 0

Add 3 to both sides:

5 x = 3 or 7 x - 6 = 0

Divide both sides by 5:

x = 3/5 or 7 x - 6 = 0

Add 6 to both sides:

x = 3/5 or 7 x = 6

Divide both sides by 7:

x = 3/5 or x = 6/7 So now how do you assign these 4 integers to a,b,c,d? How about: a=3, b=5, c=6, d=7. So (3*5) + (3*7) + (5*6) + (6*7) =108 ??. Check it please !!.

Guest Nov 14, 2017