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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?

Thank you in advance.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Additional maths O level (chapter polynomial)

hi righen

Welcome to the forum.

Your three answers for the first part look good to me. 

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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.;)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob