+0  
 
0
38
3
avatar+45 

if p and q are both prime numbers, x^2 - (8p - 10q)x +5pq = 0 has two positive integer solutions

what are all the possible prime pairs of (x,y)

hearts123  Nov 2, 2018
 #1
avatar+2786 
+2

Using brute force I come up with

 

(p,q) = (7,3), (11,3)

Rom  Nov 2, 2018
 #2
avatar+45 
+1

hey, thank you so much! would it be okay if you described the process you went through to get those answers?

hearts123  Nov 2, 2018
 #3
avatar+2786 
+1

Use the quadratic formula to get the roots in terms of p and q.

Being integers and primes and non-negative put constraints on the resulting discriminant (what's under the radical sign)

 

Solving for values that meet those constraints gets you the two pairs.

Rom  Nov 3, 2018
edited by Rom  Nov 3, 2018

33 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.