Stampboy123's maths thread

Stampboy123 SG

For each of the following, find y in terms of x

2 lg y = x-2

ln(x+y)-4x = 0

I appreciate if you can show the working.

FireIce SG

since u always have qns to ask

u can have a dedicated thread for yourself to ask

dun always open a new thread

Stampboy123 SG

So how to edit the topic?

Darkness_hacker99 SG

edited for you already

wee_ws SG

Hi,

Consider these useful results:

1. lg y = x => y = 10^x

2. ln y = x => y = e^x

3. lg (a^n) = n lg a

Thanks.

Cheers,
Wen Shih

Stampboy123 SG

Given that đś is the root of the equation x^2=2x+1, show that

A) đś^3 = 3đś-2 B) đś^4 - đś^2 = 2đś - 2

Please show working for the qn cause i need to learn through example. Thanks

wee_ws SG

Hi,

What do the boxes represent? Thanks for clarifying.

Cheers,
Wen Shih

Stampboy123 SG

it is alpha.

wee_ws SG

Hi,

I believe something is not right about the two results.

Given x^2 = 2x + 1, one can solve for alpha easily. alpha is either 1 + sqrt(2) or 1 - sqrt(2).

One can verify via substitution that the two results do not hold.

Thanks.

Cheers,
Wen Shih

wee_ws SG

Hi,

Since Îą is a root to the equation, then Îą^2 = 2Îą + 1, which is useful for our later proof.

One (correct) result we can show is Îą^3 = 5Îą + 2.

Proof:

LHS = Îą^3

= Îą. Îą^2

= Îą (2Îą + 1)

= 2Îą^2 + Îą

= 2(2Îą + 1) + Îą

= 5Îą + 2

= RHS.

Thanks.

Cheers,
Wen Shih

Stampboy123 SG

thanks wee_ws

x^2+ax < b is only satisfied by -2<x<4

Find value a and b

wee_ws SG

Hi,

Now x^2 + ax - b < 0 is satisfied by (x + 2)(x - 4) < 0, so a and b can be found easily.

Thanks.

Cheers,
Wen Shih