ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 unit (1 Viewer)

[RealiseNothing]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

equating co-efficients?

Won't work.

I'd say by looking at it he has to expand the RHS, so the x^4 will cancel out, then solve the cubic left somehow.

 

[RivalryofTroll]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Won't work.

I'd say by looking at it he has to expand the RHS, so the x^4 will cancel out, then solve the cubic left somehow.

Usually for these questions, you can form simultaneous equations to solve.

not too sure.

 

[RealiseNothing]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Wait nvm, just had another look.

Expand RHS, equate co-efficients, solve simulatenously.

Taa-daa.

 

[RealiseNothing]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Usually for these questions, you can form simultaneous equations to solve.

not too sure.

Yep, was thinking something else in my head.

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Is the answer 2 and -2?

Yes

the answers say A=-2 and B=2

 

[Sy123]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un



Right?

Doesnt matter what A and B are, as long as values are present (unless they give a restriction like A>B or something unecessary)

 

[RivalryofTroll]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Right?

Absolutely correct.

Good job.

 

[nightweaver066]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I know it has something to do with this though I do not understand what the term means or anything about this term.

Equating coefficients means comparing the coefficients on both sides of an equality sign.

E.g. If ,

it can be said that

 

[RealiseNothing]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Yes

the answers say A=-2 and B=2

Well A and B can both be either 2 or -2 (like you can swap them around, doesn't matter). Here's the ~cool~ way to do it:

Expand RHS and equate co-efficients to get:

A + B = 0

AB = -4

Instead of solving simultaneously like a nerd, do this:

Notice that they look like the sum of the roots, and the product of the roots? Well why not make them that! Make a quadratic in, say 'u', with those as the sums and products of roots:



But A + B = 0 and AB = -4, so:





Therefore A = 2 and B = -2, or the other way round.

(lol I'm not even sure if this is a coincidence, or actually a valid method).

 

[Sy123]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Well A and B can both be either 2 or -2 (like you can swap them around, doesn't matter). Here's the ~cool~ way to do it:

Expand RHS and equate co-efficients to get:

A + B = 0

AB = -4

Instead of solving simultaneously like a nerd, do this:

Notice that they look like the sum of the roots, and the product of the roots? Well why not make them that! Make a quadratic in, say 'u', with those as the sums and products of roots:



But A + B = 0 and AB = -4, so:





Therefore A = 2 and B = -2, or the other way round.

(lol I'm not even sure if this is a coincidence, or actually a valid method).

Absolutely excellent method, Im pretty sure in one the HSC Q7s for 3U they ask you to make your own quadratic equation based on Projectile Motion where you are given the sum of two things and the product of the two things.

Nice work

EDIT: Also thinking like this will most probably help and student in 4U math, to be able to think outside the box and stuff.

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I've also got a weakness for finding the domain and range for hyperbolas when they're like for example:

x-1/x-3

x/x+2

etc

Anybody have any techniques/thought process/skills on how to deal with this?

 

[nightweaver066]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I've also got a weakness for finding the domain and range for hyperbolas when they're like for example:

x-1/x-3

x/x+2

etc

Anybody have any techniques/thought process/skills on how to deal with this?

Draw a quick sketch. Probably something you're more comfortable with.

 

[RivalryofTroll]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I've also got a weakness for finding the domain and range for hyperbolas when they're like for example:

x-1/x-3

x/x+2

etc

Anybody have any techniques/thought process/skills on how to deal with this?

For denominator =/= 0

Therefore, x=/= 3 for your first one and x=/=-2 for your second one.

Denominator cannot equal zero is the key for domain. All real x except x = whatever or All real x, x=/= whatever.

For y-value, see wut happens as x approaches infinity.

y = x-1/x-3 - means y approaches 1 as x approaches infinity.

Hence, all real y, y=/= 1

 

[Sy123]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I've also got a weakness for finding the domain and range for hyperbolas when they're like for example:

x-1/x-3

x/x+2

etc

Anybody have any techniques/thought process/skills on how to deal with this?

Finding Domain is obvious for hyperbola, its pretty much what x can be, so what we are looking for is what x cant be.
For
x cannot be 3.

Therefore our domain is all real x,

For Range however, in hyperbolas, what you can do is subsitute negative and positive infinity values into your calculator (sub in very large numbers), and see where they approach, for example in that above function, when you sub in values you will notice that you will get very close to 1,
our range is hence y is all real except y cannot equal to 1.

A useful tip, that will help you in 3U further curve sketching and finding range of hyperbolas is:


Our horizontal asymptote (and the value that y cannot be) is:

This works to find horizontal asympote for any function:



The rule is:

If n<.m, the horizontal asymptote is y=0
If n=m, horizontal asypmtote is y=a/b

If n>m, use polynomial division (do not worry about this right now)



That is just the logic behind it that is all.</m,>

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Thanks so much for your help guys.

Greatly appreciate it.

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Solve the equation (x-1)^3-4(x-1)2+5(x-1)-2=0

Would you expand it first or is there a faster way?

 

[SpiralFlex]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Solve the equation (x-1)^3-4(x-1)2+5(x-1)-2=0

Would you expand it first or is there a faster way?

Solve from there.

 

[twinklegal19]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Solve from there.

the inspection method? haha yeah it's pretty cool

 

[RealiseNothing]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Solve from there.

Nice factorising there, spiral.

 

[SpiralFlex]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Nice factorising there, spiral.

+2