Is this a thing?
https://www.nytimes.com/2020/02/05/science/quadratic-equations-algebra.html
A math-only board.
https://www.nytimes.com/2020/02/05/science/quadratic-equations-algebra.html
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Paywalled.
Can someone with access to the article, summarize shat the trick is ?
>>26
"This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical.
For example, in this parabola:
y = x^2 – 4x – 5
The two solutions when y = 0 are the symmetrical points r and s, where the parabola crosses the x-axis.
The midpoint, or average, of r and s is the axis of symmetry of the parabola. We want r + s = –b, which happens when the average of r and s is –b ÷ 2. In this example: 4 ÷ 2 = 2.
The two solutions to the quadratic equation will be the axis of symmetry plus or minus an unknown amount, which we’ll call u. In this example:
r = 2 – u and s = 2 + u
To find u, we want the product of r and s to be equal to c, which in this example is –5. Rewriting r and s in terms of u:
r × s = –5
(2 – u) × (2 + u) = –5
Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
The two solutions to this quadratic equation are 2 – u and 2 + u, or –1 and 5. In other words, this parabola intersects the x-axis when x = –1 and x = 5."
>>28
>Solving that yields 22 – u2 = –5 or u2 = 9, so u = 3 works.
Solving that yields 22 – u^2 = –5 or u^2 = 9, so u = 3 works.
Sorry. Copy-and-paste mistake.
Ever since that other anonymous website made a major contribution to mathematics, I feel like we should be able to do it too. I vote that we work on the Riemann Hypothesis.
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>>3
maybe not? but, you know that's a really hard problem, right?....
do you even know anything about math?
The g-ds never give mortals possible tasks. Otherwise, they would have done it themselves.
Shouldn't we opt for something simpler first? Like developing calculus without limits or infinities - and then use that for something trivial, like plotting trajectory of a planet moving under influence of a black hole? Of course, somewhere in between we'll need to develop new theory of gravity with our new, finite, calculus.
Thank you for your wonderful contribution! Always love to see some real maths here.
e-d statements are rad
Did you know that you can use LaTeX on this website?
>>10
Although, not all things you'd expect are supported so I guess my forall symbol failed there.
Anyway, just type it like this.
%%%
some text $some latex$ more text
%%%
>>11
Of course, it doesn't work for post titles.
I love math!
I love math too!
What's your favourite theorem?
Well, it would have to be Fermat's Last, wouldn't it.......
Ummm, is it normal to know a lot of these theorems offhand?