Canadian math olympiad
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- Опубликовано: 8 дек 2023
- Hello everyone
. In this video I solved a nice problem from canadian math olympiad . If you enjoyed the video, dońt forget to subscribe!❤️
Quadratic equation
• How can you solve quad...
#calculus #math #matholympiad #algebra
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just a very complicated way to describe the golden section. Nice
The X1 case is incorrect for a different reason. X1-1/X1=1 is greater than 0
Rather X1 is incorrect because if you plug X1 back into original equation, the LHS will not equal RHS
Consider a geometric approach: think of the right hand side of the equation as the some of two sides of two different right angle triangles. The first triangle having root x being the hypotenuse and the second having root 1, or 1, as its. And the two triangles share a common length of right-angled edge of root 1/x. Draw this two triangles together taking advantage of that common edge and have the two hypotenuse on the same side. Now by showing the lengths of certain edges are in common ratio(fairly easy to see which if you actually draw it), we can say that the three triangles in the graph are all similar to one another, where the biggest triangle having root x and 1 as its right-angled edges and having x as its hypotenuse, given by the conditional equation. Applying the Pythagorean’s theorem on the biggest triangle you get x + 1 = x^2, and the rest is the same.
Thought it’s provoking to think of some equation geometrically on general, and in this specific case, better or even simpler to think like that than to what’s in the video.
If you assume the combined triangles form a 3rd right triangle, this all works out. Is there anything that indicates that they do? I think the 2 smaller triangles are only similar because x is phi, the golden ratio.
@@dugong369 Using the given lengths of the edges you can induct deduce that the three triangles are all similar to one another, thus the third triangles would also be a right angle triangle same as any one of the two original ones.
Specifically, 1 : root 1/x = x : root x. (Root x : root 1/x = x : root x also works)
@@dugong369 And also, the two original triangles are and only are similar because of they have their lengths of their edges in ratio. 1 : root 1/x : root (x-1)/x = root x : root (x^2-1)/x : root 1/x.
x turns out to be phi is and only is because of the bonding equation. Try to view the equation as a determining condition, which helps to determine how “big”the image is in absolute; the value of x is therefore determined for the same reason.
it's phi
Yes