Today, I happened upon this video for the very first time. After I read the problem, I paused the video and solved it without using any graphs, coordinates, perpendicular lines or circles. ************* Number the 4 given equations by (1), (2), (3) and (4). (I) Use determinants to "quickly" solve for a and b, in terms of m, from "equations (1) and (2) as a system". (II) As a and b satisfy equations (3) and (4), use the results from (I), I got n = ........ and n = ........., both in terms of m, from equations (3) and (4), respectively. (III) Thus, I got an equation in m alone; solve for m; then, use the results from (I) to get a and b. Coach Sjoberg, have you tried this way?
Though I haven't tried your strategy (I always try to use "elementary" strategies, as Mathcounts problems can theoretically all be solved with no math knowledge beyond Geometry), I absolutely love that you paused the video and worked through the problem on your own! Finding 2 or more methods to solve every problem is an awesome goal! Kudos!
Today, I happened upon this video for the very first time. After I read the problem, I paused the video and solved it without using any graphs, coordinates, perpendicular lines or circles.
*************
Number the 4 given equations by (1), (2), (3) and (4).
(I) Use determinants to "quickly" solve for a and b, in terms of m, from "equations (1) and (2) as a system".
(II) As a and b satisfy equations (3) and (4), use the results from (I), I got
n = ........ and n = ........., both in terms of m, from equations (3) and (4), respectively.
(III) Thus, I got an equation in m alone; solve for m; then, use the results from (I) to get
a and b.
Coach Sjoberg, have you tried this way?
Though I haven't tried your strategy (I always try to use "elementary" strategies, as Mathcounts problems can theoretically all be solved with no math knowledge beyond Geometry), I absolutely love that you paused the video and worked through the problem on your own! Finding 2 or more methods to solve every problem is an awesome goal! Kudos!
where can I find the problem pdf?
@@charlessun9100 they sell all the old competitions at Mathcounts.org