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## #1 2014-01-20 09:42:35

righen
Guest

### Additional maths O level (chapter polynomial)

Hi everyone,
Can someone help me solve this problem?

Solve this equation:
X^2 (x+3)=10x+24
Hence use a suitable substitution to solve
25x^2 (5x+3)=50x+24

The first part I was able to do! I obtain x=-2,-4, 3.
The second I am stuck.I dont know what to do?

## #2 2014-01-20 10:05:44

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Additional maths O level (chapter polynomial)

hi righen

Welcome to the forum.

So you have solved

or why not say you have solved

ie y = -2, -4 and 3.

I've made a new variable so I can use x as the variable in the second part.

If you put y = 5x in the above you get

which simplifies to

which is the second question.

So it must have solutions  y = -2, y = -4 and y = 3

which becomes

5x = -2, 5x = -4 and 5x = 3

These will give three new values for x as answers.

Let's try out just one of these to make sure this is working.  I'll take the third one.

If 5x = 3 then x = 3/5

Try in the equation

and

So LHS = RHS and we have a solution.

I'll leave you to work out the other two for yourself.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2014-01-20 10:26:23

righen
Guest

### Re: Additional maths O level (chapter polynomial)

Hi Bob,

Thank you for your quick reply and the nice welcome. You wont believe me I am actually doing a major in mathematics (its my first year) and decided to do some revision:D. To get stuck at such a low level problem is a shame.I just wanted to know what causes u to get to y=5x because I have to say I try my best to find a substitution but unfortunately I coudn't get it:(.what I try was to put both equation at 24 and equate the L.H.S of both equation to get a quadratic that give irrational roots:mad:.Anyway thank you again for the quick reply.;)

## #4 2014-01-20 12:34:03

bob bundy
Registered: 2010-06-20
Posts: 8,321

### Re: Additional maths O level (chapter polynomial)

hi righen

The clue is this:

Hence use a suitable substitution

and it helps that I've done loads of similar ones over the years.

I looked at the two equations and paired together the similar bits in my head like this:

x^2                          (x+3)             =                               10x                              +24

25x^2                     (5x+3)             =                               50x                              +24

I could see straight away that each x had become 5x and that was all I needed.

The person making up the question could have made it much nastier by multiplying out the brackets and moving the terms around a bit.  So you will have to be on the lookout for that sort of thing too.

Thus instead of the second equation you could have been given:

But it's still the same problem.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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