perplexus.info :: Just Math : Simultaneous Settlement VII

Simultaneous Settlement VII (Posted on 2023-01-08)

Each of m and n is a complex number that satisfies this set of simultaneous equations:

Without solving for m and n, determine the value of mn

Note: mn is the product of m and n, rather than their concatenations.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Easier Analytic Solution

| Comment 3 of 6 |

Rearrange the two equations

mn - 3 = n^2

mn -1 = -2m^2

Multiply the equations

(mn)^2 - 4mn +3 = -2(mn)^2

Rearrange

3(mn)^2 - 4mn +3 = 0

Use the quadratic formula to get

mn = (4 +/- sqrt(-20))/6

= (2 +/- sqrt(5)*i)/3

Posted by Steve Herman on 2023-01-08 16:32:18

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info