O-Level Additional Math

[BlurBerry]

This question appeared in my son’s Sec1 EOY paper. I’m stumped. Can anyone help? Thanks in advance.


One of the famous Arithmetic and algebraic paradoxes show the proof of 2=1

Proof of 2=1:
Assume that
a = b
Multiplying both sides by a,
a^2 = ab
Subtracting b^2 from both sides,
a^2 - b^2 = ab - b^2
Factoring both sides,
(a + b)(a - b) = b(a - b)
Dividing both sides by (a - b),
a + b = b

If now we take a = b = 1, we conclude that 2 = 1.

Analyse the above solution and explain the conceptual error that leads to the above paradox of 2 = 1.

[Pen88n]

The conceptual error lies in the fact that a=b and you are dividing both sides by (a-b) which is zero. Any equations divide by zero cannot prove anything.

[BlurBerry]

Pen88n:

The conceptual error lies in the fact that a=b and you are dividing both sides by (a-b) which is zero. Any equations divide by zero cannot prove anything.

OIC!! Thanks very much for your help.

[GreenQ]

Need help to solve this:


Solve: 1/(2-lnx)-1/(3-lnx)=6

[GreenQ]

Pls help to solve this problem: Thx!!!\t


\tIf z=x+iy, find x and y for z ̅+2=i2(z-1)

[FrekiWang]

GreenQ:

Pls help to solve this problem: Thx!!!\t


\tIf z=x+iy, find x and y for z ̅+2=i2(z-1)

Your - means *(conjugate)?

I assume you mean z*+2=2i(z-1)

x-iy+2=2i(x+iy)-2i
x+2-iy=-2y+i(2x-2)

so x+2=-2y, -y=2x-2
solve, we get x=2,y=-2.

[GreenQ]

FrekiWang:

Your - means *(conjugate)?....

Thanks. The - sign is on top of z. Help pls....

[apple_a_day]

Think simple.

If you let lnx=y, it will become a simple algebra question with:

1/(2-y) - 1/(3-y) =6

Try again, my dear

[GreenQ]

Oh yes... Thank you!!

[FrekiWang]

GreenQ:

FrekiWang:

Your - means *(conjugate)?....

Thanks. The - sign is on top of z. Help pls....

I already answered your question, but I suppose in A level, we use z* rather than z(with - on top) to represent conjugate.