Recent content by n7imo

The problem is very easy to explain, I wonder if there is a different approach that give an elegant solution.

I ended up with a system of two nonlinear equation, I talked about it here https://www.physicsforums.com/threads/a-nonlinear-equation-system.862991/ I used x =BC and y= AD. Once I found x and y I used Pythagore to find DC. But the x (or y) end up being a solution of a quartic equations ... messy

How did you approach the problem ?

Don't hesitate sharing it, I found the answer in a numerical form, but I'm curious about finding a closed form solution.

Hello, A friend of mine gave me this puzzle and I'd like to share it with you, math enthusiasts: Two ladders intersect in a point O, the first ladder is 3m long and the second one 2m. O is 1m from the ground, that is AC = 2, BD = 3 and OE = 1 (see the image bellow) Question: what's the value...

Indeed, the right resulting quartic equation is x^4 - 2x^3 - 5x^2 -10x - 5 =0. I used Cardano and Lagrange method to find the real roots, but their form is very ugly. Actually I got this equation while trying to solve a simple geometrical problem. I'll post it today on a new thread, I'm...

I'm trying to find a closed form (an algebraic solution) for the following system: x² - y² = 5 x + y = xy It's a bit tricky but I manage to end up with the quartic equation: x^4 - 2x^3 + 5x^2 -10x + 5 =0 And this is where I get stuck looking for a closed form root. Any suggestion would be...