O-Level Additional Math

[atutor2001]

iFruit:

hot_chocolate:

Please help to solve the followings:


1) The product of n whole numbers 1 x 2 x 3 x 4 x 5 x ....x (n - 1) x n has 28 consecutive zeros. Find the largest value of n.

In a factorial, every multiple of 5 will contribute one zero at the end

for example, 1x2x3x4x5 = 120, 120x6x7x8x9x10 = [something]00

In addition every multiple of 25 will contribute one extra zero

25x24, 50x48, 75 x 72, 100x99 etc.

So 120! would have 120/5 = 24 zeros contributed by multiples of 5,

and 4 extra zeros contributed by multiples of 25 (25, 50, 75, 100) with 28 zeros (24+4) at the end.

So the largest factorial with 28 consecutive zeros is 124! --> n = 124

Hi iFruit

You are really good!

[hot_chocolate]

Hi iFruit,


The answers are correct! Thanks for the solutions.

Agree with atutor2001, you're really good.

[iFruit]

hot_chocolate:

Hi iFruit,


The answers are correct! Thanks for the solutions.

Agree with atutor2001, you're really good.

Thank you atutor2001 and hot_chocolate. You are very kind.

[emerald]

Hi, pls help to solve:


(2h - 7k)(3k - 1)(3 - h)


Thanks.

[iFruit]

emerald:

Hi, pls help to solve:


(2h - 7k)(3k - 1)(3 - h)


Thanks.

Hi emerald,

Is the question complete? Could you clarify?

[emerald]

iFruit:

emerald:

Hi, pls help to solve:


(2h - 7k)(3k - 1)(3 - h)


Thanks.

Hi emerald,

Is the question complete? Could you clarify?

Hi iFruit,

This is the given question but maybe there's some problem with it cos my dd couldn't solve it. Anyway, thanks for responding.

[OK Lor]

Hi,


The question is a little off topic, please help to factorise x⁴+ 4

Thanks.

[iFruit]

OK Lor:

Hi,


The question is a little off topic, please help to factorise x⁴+ 4

Thanks.

x⁴+ 4 = x⁴+ 4+4x²-4x² = (x²+2)² - (2x)² = (x²+2x+2)(x²-2x+2)

[OK Lor]

Hi iFruit,


Thank you very much

[atutor2001]

iFruit:

OK Lor:

Hi,


The question is a little off topic, please help to factorise x⁴+ 4

Thanks.

x⁴+ 4 = x⁴+ 4+4x²-4x² = (x²+2)² - (2x)² = (x²+2x+2)(x²-2x+2)

Hi iFruit

I really enjoy your solution, it appears so simple once the approach is correct.

Just curious, is the above approach covered in normal O level course work for A math (it appears as a modification to \"completing the square\" to me) or is it something that we gain through more exposure to mathematical problems.

Regards