 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Real Variable Validation (Posted on 2016-06-11) Each of P, Q and R is a positive real number satisfying this system of equations:

P + Q = 13, and:
Q2 + R2 - Q*R = 25, and:
P2 + R2 + P*R = 144

Find R.

 No Solution Yet Submitted by K Sengupta No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: Solution Comment 4 of 4 | (In reply to Solution by Brian Smith)

'Then substitute into the first equation:
(R +/- sqrt(100-3R^2))/2 + (R +/- sqrt(576-3R^2))/2 = 13'

To be exact: ((576-3R^2)^(1/2)-R)/2+(R + (100-3R^2)^(1/2))/2 =13

Then ((100-3R^2)^(1/2)+(576-3R^2)^(1/2))^2 = 26^2, and there is a sort of quartic, which cancels: (300-9R^2)(192-R^2) = 9R^4

But if so, then 57600-2028R^2 = 0; R^2 = 4800/169: R = 40*3^(1/2)/13, as expected.

 Posted by broll on 2016-06-12 05:13:37 Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information