A-Level Maths [Help] - Surds

So i had this question
Show that

[br]f(x) = (3-4\sqrt{x})^2[br]Show that f(x) = 9x^{-1/2} + Ax^{1/2} + B[br]where A and B are constants[br]

I done the first bit - expanding
Which leaves me with

Unparseable latex formula:

\frac{9-24\sqrt{x} +16x}{\sqrt{x}} \[br]

I know the answer etc. as it saids it in the question, I just don't undertstand how you divide by a square root

(edited 7 years ago)

bump - fixed formats

Think about what root x would be if you wrote it as x to a power
Then actually try to divide each term of the numerator by this and see what you get - use power laws

Reply 3

RDKGames

Study Forum Helper

Original post by AdeptDz

So i had this question
Show that

[br]f(x) = (3-4\sqrt{x})^2[br]Show that f(x) = 9x^{-1/2} + Ax^{1/2} + B[br]where A and B are constants[br]

I done the first bit - expanding
Which leaves me with

Unparseable latex formula:

\frac{9-24\sqrt{x} +16x}{\sqrt{x}} \[br]

I know the answer etc. as it saids it in the question, I just don't undertstand how you divide by a square root

Divide each term by

\sqrt{x}

and remember that

\sqrt{x}=x^{1/2}

also

\frac{1}{a}=a^{-1}

Also f(x) cannot be in that form unless it is

\displaystyle \frac{f(x)}{\sqrt{x}}

(edited 7 years ago)

Reply 4

BobBobson

\frac{9-24\sqrt{x}+16x} {\sqrt{x}}

can be written as:

\frac{9} {\sqrt{x}} + \frac{-24\sqrt{x}} {\sqrt{x}} + \frac{16x}{\sqrt{x}}

. See if that helps you.

If you need some extra help with figuring out A:

Spoiler

Reply 5

AdeptDz

Original post by RDKGames

Divide each term by

\sqrt{x}

and remember that

\sqrt{x}=x^{1/2}

also

\frac{1}{a}=a^{-1}

Yh thanks, i understand what you said. So okay it saids the answer to:

\frac {9}{\sqrt{x}} = 9x^{-1/2}

So like it is

9 / x^{1/2} =

or is that basically saying 9/a so would it be

9x^{-1/2}

If that isn't correct then I still don't get it :s-smilie:

(edited 7 years ago)

Reply 6

AdeptDz

Original post by BobBobson

\frac{9-24\sqrt{x}+16x} {\sqrt{x}}

can be written as:

\frac{9} {\sqrt{x}} + \frac{-24\sqrt{x}} {\sqrt{x}} + \frac{16x}{\sqrt{x}}

. See if that helps you.

If you need some extra help with figuring out A:

Spoiler

Thanks, (@ spoiler) I should know this but I still can't figure out why that is the case

Edit: Ohh i think i understand now, it is basically like saying