GCSE Further maths questions: surds

Really stuck on this further maths question:

3/(Sqrt[5] + x) = 3 Sqrt[5] + y

Would really appreciate an explanation and the solutions. Thanks in advance!

(this is an A** question)

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Reply 1

gosforthtsr

What does the question want? Simplification or the solution to x or y?

Reply 2

Felhasacharizard

Original post by gosforthtsr

What does the question want? Simplification or the solution to x or y?

That's what i wanted to know too aha! :colondollar:

solution to x and y

Original post by Felhasacharizard

That's what i wanted to know too aha! :colondollar:

can you solve the question if the question is asking for the solutions for x and y?

Reply 5

Felhasacharizard

Original post by js15398

can you solve the question if the question is asking for the solutions for x and y?

Does OP have the answers to check, I did manage to get solutions which are x=2 y=-6 I'm not sure whether these are right though? Can anyone else confirm?? :s-smilie:

(edited 9 years ago)

Reply 6

lerjj

Original post by js15398

Really stuck on this further maths question:

3/(Sqrt[5] + x) = 3 Sqrt[5] + y

Would really appreciate an explanation and the solutions. Thanks in advance!

(this is an A** question)

What have you tried to do? The first thing you should be looking at is rationalising or cross multiplying from the looks of it. Seeing as how you've got two variables and one equation though, looks like you need to simplify, not solve.

EDIT: are you sure the question is

\dfrac{3}{\sqrt{5}+x}=3\sqrt{5}+y

(edited 9 years ago)

Reply 7

js15398

Original post by lerjj

\dfrac{3}{\sqrt{5}+x}=3\sqrt{5}+y

yes it is, I have tried to rationalise etc. but haven't really got close to getting an answer

Reply 8

js15398

Original post by Felhasacharizard

Does OP have the answers to check, I did manage to get solutions which are x=2 y=-6 I'm not sure whether these are right though? Can anyone else confirm?? :s-smilie:

The book doesn't have answers at the back but I checked on wolfram alpha- it says the solution is:

x=-2, y=6

x=2, y=-6

how did you do it?

Reply 9

lerjj

Original post by js15398

yes it is, I have tried to rationalise etc. but haven't really got close to getting an answer

What is the precise wording of the question? You have more variables than equations atm so it's kind of important to know whether x and y have to be integers, or whether there's an indentity sign etc.

Or whether it actually wants you to solve.

Reply 10

Felhasacharizard

Original post by js15398

The book doesn't have answers at the back but I checked on wolfram alpha- it says the solution is:

x=-2, y=6

x=2, y=-6

how did you do it?

1 sec let me write it out neatly and post it as a picture. I probably went round an odd path if there are meant to be two solutions, but ill post it anyways.

Reply 11

js15398

Original post by lerjj

the precise wording is "work out the values of x and y such that: (with the equation) "

Reply 12

Felhasacharizard

Original post by js15398

The book doesn't have answers at the back but I checked on wolfram alpha- it says the solution is:

x=-2, y=6

x=2, y=-6

how did you do it?

Ah whilst rewriting i have managed to confuse myself, this might take a while soz you basically rationalise then make y the subject, then substitute y back into it and solve x. Then you can substitute x to find the real value of y.

yes got it

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Reply 15

Felhasacharizard

ImageUploadedByStudent Room1411228488.576476.jpg

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Reply 16

Felhasacharizard

Apologies for poor lighting, messy work etc. haha! I managed to get the two answers (yay) Any questions???

Reply 17

js15398

Original post by Felhasacharizard

Posted from TSR Mobile

Thank you! just wanted to ask, with regards to the first page of workings, can you cancel the 3sqrt5 from the numerator and the denominator?

Reply 18

Felhasacharizard

Original post by js15398

Thank you! just wanted to ask, with regards to the first page of workings, can you cancel the 3sqrt5 from the numerator and the denominator?

Welcome - love helping!! :biggrin:

Which step/line of working?

If it's the second line, no you can't because when you rationalise you are trying to get rid of the bottom surd, if you cancelled, you would end up doing nothing because you would be undoing the rationalisation and would end up with the starting fraction again.