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# Maths. Watch

1. I feel like I am missing the complete obvious here but how do I find A,B.C and D?

1/(x^2+1)^4 = d/dx*(Ax^5+Bx^3+Cx)/(x^2+1)^3 + Dx^6/(x^2+1)^4

I differentiated it and subbed in x = 1 but in the end all I'm left with is constants and no way of solving them......there must be a step i'm overlooking?

THanks.
2. What is the actual question? Is it just to find A, B, C and D?
3. it might work ..but try integrating LHS instead of differentiating RHS ..seems much easier and then do all the rearranging stuff
4. (Original post by Chelle-belle)
What is the actual question? Is it just to find A, B, C and D?
well the first part of the question is "show that for 0<x<1 the largest value of x^6/(x^2+1)^4 is 1/16.

This is the second part that I have given in my OP.

btw, it's supposed to be greater than or equal to and not greater than!
5. (Original post by rbnphlp)
it might work ..but try integrating LHS instead of differentiating RHS ..seems much easier and then do all the rearranging stuff
How will that help?
6. (Original post by boromir9111)
well the first part of the question is "show that for 0<x<1 the largest value of x^6/(x^2+1)^4 is 1/16.

This is the second part that I have given in my OP.

btw, it's supposed to be greater than or equal to and not greater than!
ok in that case , your method is probably the safe bet ..just carefully rearrange everything and compare coefficients just like you would do in partial fractions ..(post your working if you wish)
7. Well after differentiating it and subbing in x = 1, I get

1/16 = (4A - 6C + D)/16

I can't see anyway of solving that?
8. (Original post by boromir9111)
Well after differentiating it and subbing in x = 1, I get

1/16 = (4A - 6C + D)/16

I can't see anyway of solving that?
ok ..Im not sure how you got that ..

post you working ..
before substituting in x , rearrange so that, say you get something like Ax^2+bx+C=1
now compare coffecents , here you know Ax^2=0,bx=0 and C=1.
9. (Original post by boromir9111)
Well after differentiating it and subbing in x = 1, I get

1 = 4A - 6C + D

I can't see anyway of solving that?
Can you post the differentiated version so we don't have to do it lol
10. Lol. Seems like I have totally forgotten how to do partial fractions......thanks mate!
11. (Original post by Chelle-belle)
Can you post the differentiated version so we don't have to do it lol
I may be wrong on this but I get:

((Ax^5 + Bx^3 + Cx)*-6x)/(x^2+1)^2 + (5Ax^4 + 3Bx^2 + C)/(x^2+1)^3 +

Dx^6/(x^2+1)^4
12. I'm assuming this is a STEP I question?
13. (Original post by boromir9111)
Well after differentiating it and subbing in x = 1
Not that I have a solution (sorry) but you subbed x=1 into

?
14. (Original post by Farhan.Hanif93)
I'm assuming this is a STEP I question?
Yeah....I kinda figured you would know that! I came across and it intrigued me and now it's annoying me!
15. (Original post by Chelle-belle)
Not that I have a solution (sorry) but you subbed x=1 into

?

Never mind!!!
17. (Original post by boromir9111)
From there, combine it into one fraction. Then equate the numerators of the LHS and RHS. Then expand and rearrange that expression to obtain a polynomial of degree 6. You should be able to find the value of C immediately from there. Then equate the coefficients of each power of x to what they are on the RHS to obtain a system of simultaneous equations (IIRC they should be zeroes). The values should follow from there easily. This is just an algebraic exercise, rather than a puzzling problem tbh. All you need to do is be careful with your algebra.
18. (Original post by Farhan.Hanif93)
From there, combine it into one fraction. Then equate the numerators of the LHS and RHS. Then expand and rearrange that expression to obtain a polynomial of degree 6. You should be able to find the value of C immediately from there. Then equate the coefficients of each power of x to what they are on the RHS to obtain a system of simultaneous equations (IIRC they should be zeroes). The values should follow from there easily. This is just an algebraic exercise, rather than a puzzling problem tbh. All you need to do is be careful with your algebra.
I was hoping I didn't have to do that lol.....but yeah, I get it now......thanks a lot buddy!
19. (Original post by boromir9111)
Mmm could have been me (I tend to complete arithmetic stupidly by mistake) but try it again.
20. (Original post by Chelle-belle)
Mmm could have been me (I tend to complete arithmetic stupidly by mistake) but try it again.
Yeah, I know how to do it now....thanks anyway!

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