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I think I've stumbled upon an idea which works. Anyone else noticed this before?

So I'm not gonna go out on a limb and say I'm the first to discover this or that this is incredibly helpful because it will rarely come up. Upon doing a test yourself question for Aqa Pure Core 4 Chapter 5 (Cartesian/Parametric Equations) I discovered that; (a^2)((c+d)/a)^2=(c+d)^2. Does that make any sense? It's hard to type it out correctly but like I said this will rarely come up but I managed to find an alternative answer to the text book. Has anyone else noticed this before or this just really obvious? lol
Reply 1
Original post by WillFarndon
So I'm not gonna go out on a limb and say I'm the first to discover this or that this is incredibly helpful because it will rarely come up. Upon doing a test yourself question for Aqa Pure Core 4 Chapter 5 (Cartesian/Parametric Equations) I discovered that; (a^2)((c+d)/a)^2=(c+d)^2. Does that make any sense? It's hard to type it out correctly but like I said this will rarely come up but I managed to find an alternative answer to the text book. Has anyone else noticed this before or this just really obvious? lol

a2×(c+da)2=a2×(c+d)2a2=(c+d)2\displaystyle a^2 \times \left(\frac{c+d}{a}\right)^2 = a^2 \times \frac{(c+d)^2}{a^2} = (c+d)^2

I'm not sure what you mean when you say it's an alternative answer to your textbook.
a2((c+d)a)2=a2((c+d)2a2)=(c+d)2a^2 \left( \frac{(c+d)}{a} \right)^2 = a^2 \left (\frac{(c+d)^2}{a^2} \right) = (c+d)^2

Edit: Second consecutive post I got ninjaed.
Original post by notnek
a2×(c+da)2=a2×(c+d)2a2=(c+d)2\displaystyle a^2 \times \left(\frac{c+d}{a}\right)^2 = a^2 \times \frac{(c+d)^2}{a^2} = (c+d)^2

I'm not sure what you mean when you say it's an alternative answer to your textbook.


Basically he thinks that this is some exceedingly important and non-trivial result, when in fact it follows simply by basic algebra. WillFarndon, this result is indeed really obvious.

Original post by WillFarndon
So I'm not gonna go out on a limb and say I'm the first to discover this or that this is incredibly helpful because it will rarely come up. Upon doing a test yourself question for Aqa Pure Core 4 Chapter 5 (Cartesian/Parametric Equations) I discovered that; (a^2)((c+d)/a)^2=(c+d)^2. Does that make any sense? It's hard to type it out correctly but like I said this will rarely come up but I managed to find an alternative answer to the text book. Has anyone else noticed this before or this just really obvious? lol
Reply 4
So you discovered how powers and fractions work..
Reply 5
lol yer, Well hey, I was proud of myself when I figured it out :P Sorry if it seemed 'obvious'...(that really did hurt lol)
Reply 6
Original post by WillFarndon
lol yer, Well hey, I was proud of myself when I figured it out :P Sorry if it seemed 'obvious'...(that really did hurt lol)

I remember coming up with stuff when I was doing maths at school. I used to wonder if I was the only one who had thought of it. It generally turned out that I wasn't!

But don't let this put you off :smile:
Reply 7
Original post by WillFarndon
lol yer, Well hey, I was proud of myself when I figured it out :P Sorry if it seemed 'obvious'...(that really did hurt lol)


Original post by notnek
I remember coming up with stuff when I was doing maths at school. I used to wonder if I was the only one who had thought of it. It generally turned out that I wasn't!

But don't let this put you off :smile:


I don't see what the problem with figuring out 'obvious things' is. The thing that matters is that you discovered them without guidance.

Richard Feynman would use to draw lots of triangles for fun and by playing around with the angles, he ended up proving all the common trig identities himself, that the squares of the sine and cosine of the same angle in a triangle summed to 1, etc... just because they were obvious facts didn't make it any less impressible that you did it by yourself. :smile:

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