
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 6th, 2016, 02:32 PM  #1 
Newbie Joined: Apr 2016 From: Waterbury, CT Posts: 2 Thanks: 0  Can you explain to me in details ?
QUESTION : Two integers k and p check the relationship k + p = 20 and k * p = 91. What is the value of k² + p² ? ANSWER : k and p have the values 13 and 7, hence k² + p² = 13² + 7² = 218. I still do not understand why k = 13 and p = 7. Could you give me a hint or explain to me in details please ? Thank you in advance for your answer ! 
April 6th, 2016, 02:38 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,770 Thanks: 1424 
simultaneous equations ... $k+p=20 \implies k = 20p$ $kp = 91 \implies (20p)p = 91$ $(20p)p = 91$ $0 = p^2  20p + 91$ factor the quadratic ... $0 = (p  13)(p  7)$ $p$ could be 13, which means $k=7$ or $p$ could be 7, which means $k=13$ 
April 6th, 2016, 02:41 PM  #3 
Newbie Joined: Apr 2016 From: Waterbury, CT Posts: 2 Thanks: 0 
Thank you for your fast and clear answer !

April 6th, 2016, 02:41 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,889 Thanks: 767 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
So $\displaystyle kp = 91 \implies (20  p)p = 20p  p^2 = 91$ Solve for p. Then k = 20  p. Note: We get twin solutions (p, k) = (13, 7) and (p, k) = (7, 13). Obviously these are equivalent. Dan  
April 6th, 2016, 04:50 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra 
There's no need to calculate $k$ or $ p$: $k^2+p^2=(k+p)^22kp=20^22\times 91=400182=218$ 

Tags 
details, explain, integer, relationship, values 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Can someone explain this?  shreddinglicks  Calculus  1  December 16th, 2014 05:56 PM 
Problem of confidence in waiting, see details  zacharyt  Advanced Statistics  1  January 11th, 2014 11:31 PM 
problem with algebra question .. details inside :)  nishbhatt87  Algebra  11  August 6th, 2012 04:18 PM 
Details of calculation a limit  bigli  Calculus  0  March 4th, 2012 10:51 PM 