Scroll to see replies
Original post by 333obi
Can someone please help with the following questions:
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
They're quadratics in disguise, make a substitution of y=x^2.
Posted from TSR Mobile
Original post by 333obi
Can someone please help with the following questions:
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
Presumably you meant
a) x^4 - 5x^2 + 4 = 0
b) x^4 - 7x^2 + 12 = 0
Try letting y=x^2. You will then see the factorisation more easily.
Original post by BabyMaths
Presumably you meant
a) x^4 - 5x^2 + 4 = 0
b) x^4 - 7x^2 + 12 = 0
Try letting y=x^2. You will then see the factorisation more easily.
a) x^4 - 5x^2 + 4 = 0
b) x^4 - 7x^2 + 12 = 0
Try letting y=x^2. You will then see the factorisation more easily.
x^2= x^4 - 5x^2 + 4
Do you mean like this?
Original post by 333obi
x^2= x^4 - 5x^2 + 4
Do you mean like this?
Do you mean like this?
No, do not worry about the substitution
You have
Which is the same as
Which can be factorised like this
Can you finish it from there to get your 4 possible answers?
Note - those who suggest substitution would take my second line and turn it into
Giving giving the same 4 answers
(edited 10 years ago)
Original post by 333obi
x^2= x^4 - 5x^2 + 4
Do you mean like this?
Do you mean like this?
What? No, it should equal 0, so I don't know where you've got this from.
Wherever you see an x^2 term, replace it with y, and remember what is equal to.
Posted from TSR Mobile
Original post by majmuh24
What? No, it should equal 0, so I don't know where you've got this from.
OP IGNORE THIS POST
He got this because you introduced an idea that was new to him and he related it to what he knows
Functions are frequently written as y=f(x) and you told him y=x^2 so he put the 2 equations together
I am not a fan of this substitution method, choosing y as the parameter adds to my dislike
Original post by TenOfThem
OP IGNORE THIS POST
He got this because you introduced an idea that was new to him and he related it to what he knows
Functions are frequently written as y=f(x) and you told him y=x^2 so he put the 2 equations together
I am not a fan of this substitution method, choosing y as the parameter adds to my dislike
He got this because you introduced an idea that was new to him and he related it to what he knows
Functions are frequently written as y=f(x) and you told him y=x^2 so he put the 2 equations together
I am not a fan of this substitution method, choosing y as the parameter adds to my dislike
I assume because he wanted to solve for x, that it was an equation.
I didn't think of it like that, but I can't see where the function was taken to be y. What about ?
Why? IMO changing to a quadratic makes it a lot simpler if you can't spot it straight away.
Posted from TSR Mobile
(edited 10 years ago)
Original post by TenOfThem
OP IGNORE THIS POST
He got this because you introduced an idea that was new to him and he related it to what he knows
Functions are frequently written as y=f(x) and you told him y=x^2 so he put the 2 equations together
I am not a fan of this substitution method, choosing y as the parameter adds to my dislike
He got this because you introduced an idea that was new to him and he related it to what he knows
Functions are frequently written as y=f(x) and you told him y=x^2 so he put the 2 equations together
I am not a fan of this substitution method, choosing y as the parameter adds to my dislike
What's wrong with y?
Next time I'll suggest , just for you.
I find
(edited 10 years ago)
Original post by majmuh24
I assume because he wanted to solve for x, that it was an equation.
I didn't think of it like that, but I cca
I didn't think of it like that, but I cca
I think it was but he is confused and I think it was an easy go to error
cca?
Courtney Cox Arquette?
Original post by TenOfThem
I think it was but he is confused and I think it was an easy go to error
cca?
Courtney Cox Arquette?
cca?
Courtney Cox Arquette?
I was on my phone and hit the send button by accident, I've changed it now
Posted from TSR Mobile
Original post by BabyMaths
What's wrong with y?
It has its own purpose
Next time I'll suggest , just for you.
Ta
I find
I know what you mean - I tend to teach straight factorisation and use substitution as a back up
I tend to capitalise the X as my choice
(edited 10 years ago)
Original post by majmuh24
Yeah I saw
I am old - any 3 letters and I check on a www slang site lol
Original post by majmuh24
Why? IMO changing to a quadratic makes it a lot simpler if you can't spot it straight away.
Why? IMO changing to a quadratic makes it a lot simpler if you can't spot it straight away.
Mainly because the student who needs to do this frequently is the type of student who will forget to answer the question once they have found the values of y
I see this often on here especially when the quadratic was a trig equation
Posted from TSR Mobile
So if you let x = y^2 you will get a normal quadratic .
So if you let x = y^2 you will get a normal quadratic .
Original post by hasan6091
If you do that you would have equations that involved a polynomial of order 8 - probably not a good idea
Original post by hasan6091
Other way around
Posted from TSR Mobile
Original post by 333obi
Can someone please help with the following questions:
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
Solve for x
a) x^4 - 5x^2 + 4
b) x^4 - 7x^2 + 12
c) x^4= 4x^2 + 5
a) x^4 - 5x^2 + 4 = 0
Therefore,
(x^2 - 4)(x^2 - 1) = 0
Therefore,
either x^2 - 4 = 0, or x^2 - 1 = 0
Therefore,
Either x = +/- 2, or x = +/- 1
The rest are up to you to solve. Goodluck
Original post by TenOfThem
No, do not worry about the substitution
You have
Which is the same as
Which can be factorised like this
Can you finish it from there to get your 4 possible answers?
Note - those who suggest substitution would take my second line and turn it into
Giving giving the same 4 answers
You have
Which is the same as
Which can be factorised like this
Can you finish it from there to get your 4 possible answers?
Note - those who suggest substitution would take my second line and turn it into
Giving giving the same 4 answers
If I was to use their method and solve It like this:-
a)
x^4 - 5x^2 + 4
(x^2)^2 - 5(x^2) + 4 = 0
y^2 - 5y^2 + 4
(y - 4)(y - 1) = 0
Would I then not just get 2 answers for y, y= 4 y= 1.
Quick Reply
Related discussions
- pure 3 trig is killing me
- Mathematics Quadratics
- Trigonometry
- AS level Maths (pure) - HELP ME wtf is this question
- Numerical solution
- weird cosine question
- Help with a simultaneous equation PLEASE
- further maths question
- An inequation
- Algebraic problem - The answer is 35p per book I just need the steps to get that answ
- math help alevel trigonometry
- Question
- Solving Logarithms help
- A level math questions
- Maths Problem
- Laws of logarithms
- Quadratic equations
- 3x^(-1/2) - 2rootx + 4 / 5x = 1 / rootx
- Further maths core pure roots of polynomials question.
- Knowing which particular integral to use for ordinary differential equations
Latest
Last reply 1 minute ago
Official University College London Applicant Thread for 2024Last reply 7 minutes ago
AQA GCSE English Literature Paper 1 (8702/1) - 13th May 2024 [Exam Chat]Last reply 28 minutes ago
Official: University of Bristol A100 2024 Entry ApplicantsLast reply 56 minutes ago
2023 ** Borders and Enforcement, Crime & Compliance - ICE - Immigration OfficersLast reply 1 hour ago
Official University of Edinburgh Applicant Thread for 2024Last reply 1 hour ago
Can I do economics degree without a level maths?Last reply 1 hour ago
BAE systems degree apprenticeships September 2024Last reply 2 hours ago
Government Social Research Placement interview questionsLast reply 2 hours ago
Official University of St Andrews Applicant Thread for 2024Trending
Last reply 1 week ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 1 week ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
