Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

I got caught out by that in 3rd or 4th form. It should have made me realise I wasn't actually top of the class by a country kilometre

Reminds me of

Select to expand quote

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Divide both sides by (A-B)? Divide by zero doesnt work in maths

Nice spot. Even my specialist kids take a while to see that one ....

Select to expand quote

Poodle said..

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Divide both sides by (A-B)? Divide by zero doesnt work in maths

I am afraid that Mathematics could accomplish that ( divide by 0) but not on primary school math level and end result will not be never as suggested at very end.
But here is nice example what we could do within our degree in mathematics without the bending rules

I never understood the need to replace numbers with letters. The whole exercise (algebra) is moot/pointless and confusing, (to my mind).

Select to expand quote

Subsonic said..
I never understood the need to replace numbers with letters. The whole exercise (algebra) is moot/pointless and confusing, (to my mind).

I'm sure you're just joking, but algebra "letters" are just place holders for numbers or values.

I'm sure you use it everyday...

s = d/t

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Kamikuza said..

I use this everyday
s = d/t

then you runs into difficulty when your speed comes around 300,000 km/s
that example illustrate difference when
-kid want to count apples on the table using your algebra to
-situation when you want to describe real world ( in physics)
Your formula may be useful at first but useless in second .

Select to expand quote

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Here is why Harrow could be right anyway:
medium.com/starts-with-a-bang/the-strong-cp-problem-is-the-most-underrated-puzzle-in-all-of-physics-91f387ee5c94

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Macroscien said..

Poodle said..

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Divide both sides by (A-B)? Divide by zero doesnt work in maths

I am afraid that Mathematics could accomplish that ( divide by 0) but not on primary school math level and end result will not be never as suggested at very end.
But here is nice example what we could do within our degree in mathematics without the bending rules

I get 2030. 5 X 6 X 7 = 210
210 + 10 - 17 = 203
203 X 10 = 2030

Select to expand quote

Subsonic said..
I never understood the need to replace numbers with letters. The whole exercise (algebra) is moot/pointless and confusing, (to my mind).

LOL. Confusing it may be, but pointless it is not. Without algebra it would be very hard to write computer programs, and without computer programs we wouldn't be here chatting in one now...

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Mr Milk said..

Macroscien said..

Poodle said..

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Divide both sides by (A-B)? Divide by zero doesnt work in maths

I am afraid that Mathematics could accomplish that ( divide by 0) but not on primary school math level and end result will not be never as suggested at very end.
But here is nice example what we could do within our degree in mathematics without the bending rules

I get 2030. 5 X 6 X 7 = 210
210 + 10 - 17 = 203
203 X 10 = 2030

it's 1x2, not 1+2. So it's 210 + 9 - 17 using your grouping, 202. x10 = 2020

Select to expand quote

Mr Milk said..

Macroscien said..

Poodle said..

Harrow said..
Let A = B,

-A.B = -B^2 (multiply both sides by minus B)

A^2 - A.B = A^2 - B^2 (add A-squared to both sides)

A.(A-B) = (A+B).(A-B) (factorise)

A = A + B (divide both sides by (A-B))

A = 2.A (substitute A = B, from the initial assumption)

1 = 2 (divide both sides by A)

q.e.d.

Divide both sides by (A-B)? Divide by zero doesnt work in maths

I am afraid that Mathematics could accomplish that ( divide by 0) but not on primary school math level and end result will not be never as suggested at very end.
But here is nice example what we could do within our degree in mathematics without the bending rules

I get 2030. 5 X 6 X 7 = 210
210 + 10 - 17 = 203
203 X 10 = 2030

You forgot the 2

Aha. I need glasses!