Math Is Fun Forum

I see this, is it then that the answer the book suggests is a simplified version of my answer?  If so, what is the common method to simplify?

Okay, that's brilliant and I understand how to do it! Thanks.

Could you have a look at my working out here? I'm not sure where I have gone wrong:

Find the points where the given line meets the given curve:

2x - 5y + 17 = 0   meets     xy = 6

Firstly I get y on its own:

5y = 2x + 17                       y = 6/x

y = 2/5x + 17/5

Now I can place the two side by side:

2/5x + 17/5 = 6/x

Now I balance and collect all the terms:

2/5x^2 + 17/5x = 6

2x^2 + 17x = 30

2x^2 + 17x - 30 = 0

Now I find two numbers whose sum is 17 and product is 2*-30 (or -60).  These two numbers are +20 and -3, I re-write the quadratic:

2x^2 - 20x + 3x - 30 = 0

Now I take out the common factor of the first two numbers, then the second two numbers making sure that both sets of brackets are the same:

2x^2 - 20x         + 3x - 30        = 0
2x(x-10)             + 3(x-10)       = 0

This leaves me with:
(2x+3)(x-10)

So x=10 or x=-3/2

I substitute these values into y=6/x to give me

y=6/10   and     y=6/(-3/2)=-4

So the answer should be that the line intersects the curve at (10, 6/10) and (-3/2, -4).  My book gives the answers with the signs reversed!:

(3/2, 4) and (-10, -3/5)

Whose signs are backwards?

Edit:

My signs are wrong Thanks again!

Aha! So I just substitute the value of y into the first equation?  Thankyou luca

3x - 10 = 4 - 1/2x
7/2x = 14
7x = 28
x = 4!

Thanks anyway

Q: Why are pirates pirates?

A: Because they ARRRR!

I still don't understand this.  So far the book has covered how to sketch the graphs of y=x^2, y=x^3 and y=1/x and how to translate and scale them.  It also taught us how to find the vertex point and the points where it intersects the axis.  If the question is asking me for the y value at x=-1 then, following what the book has taught so far, I don't know how to do it.
I can work the answer out because I am past this point in the book, I don't know how to work it out using any of the methods the book has taught so far:
Factorising and
Completing the Square

Any ideas?

It's a curve, not a straight line.  I don't have the book to hand but it must be x(1-x), typo on my part .  The curve is a curve of x².
x(1-x)
-x² + x

If you plot this curve on an axis you can read out the minimum and maximum co-ords of the points between x = -1 and x = 1 i.e. (-1, y), (1, y) and the vertex (1/2, 1/4).

Is it asking for the maximum and minimum points of the curve between x = -1 and x = 1 on the axis?  i.e. the maximum point of the curve is (1/2, 1/4) and then the two corresponding points at (-1, y) and (1, y)?

I have not been taught this method yet but it may appear soon.  Thanks a lot for the help though