HSC Mathematics Marathon (1 Viewer)

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Last year I started a Preliminary Maths Marathon which went for almost 40 pages until BoS died :evilfire: I might get a moderator to merge the threads when BoS is restored for a huge epic thread :spin:

Anyway, I found it was a great way to revise with other BoSers, rules are simple, answer a question then post a new one.

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daesol

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Solution to above question:
Let the roots be @/r, @, @r (@ is alpha)
product of roots: @@@ = -d/a......................................(i) (where @@@ = @ cubed)
sum of roots 2 at a time: @@( 1/r + 1 + r) = c/a..............(ii)
sum of roots: @( 1/r + 1 + r) = -b/a...............................(iii)

(ii)/(iii): @@( 1/r + 1 + r)/@( 1/r + 1 + r) = (c/a) / (-b/a)
@ = -c/b

Sub into (i): @@@ = -ccc/bbb = -d/a
Rearranging, accc - bbbd = 0.

New question:
Integrate e^(sqrt x) w.r.t.x using a suitable substitution. [From SK Patel's Excel book]

ps. I need to learn latex xD
 

jyu

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let u=e^(sqrt x), integrate e^(sqrt x) w.r.t.x =integrate 2lnu du = 2(u lnu - u) +c = 2e^(sqrt x)[sqrt x - 1] + c

hope it is right


Now pass on to you
Is there a cartesian equation for |z + i| + |z - i| = 1?
 
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jyu

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Now pass on to you
Is there a cartesian equation for |z + i| + |z - i| = 1?
 
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The smallest possible value of |z+i|+|z-1| is 2 (the straight line that joins them).
 
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lol^ thats a tough one, and if you really want you can just not bother about it evaluating it with the limits, because thats just boring calculator work.

If that is too hard heres an easier one, and one which is more likely to come up on the hsc paper

integrate : ( 4x^2-15x +29 ) / [ (x-5)(x^2-4x+13) ] dx
 

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