Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Can you think of any different ways to solve this?

Looks like he wants this:

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Can you think of any different ways to solve this?

I put it in M and got 15116544/306075025.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Can you think of any different ways to solve this?

Hi; Me too!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Can you think of any different ways to solve this?

The value of (x - 4)(y + 3) is - 10

Work out the possible pairs of values for x and y

I looked at this and couldn't think of any procedure to solve this but it says the two brackets = -10 so you got to make them multiply to make - 10. So I just used some trial and error method  so I have to make them both = 10. 10 has factors of 1 and 10, 2 and 5. How many different ways can I make 1,2, 10, and 5 in each bracket.

For x
5 -4 = 1
3 -4 = -1
6 -4 = 2
2 - 4 = -2 
9 - 4 = 5
14 - 4 = 10
-6 - 4 = - 10

So I can tell there's 7 different ways. The I just match the y with the other factor

for y
-13 + 3 = 10         so when x = 5, y = -13 and so on
7 + 3 = 10
-8 + 3 = -5

If it is a Diophantine equation, I am getting:
x= -6    y= -4
x= -1    y= -5
x= 2     y= -8
x= 3     y= -13
x= 5     y= 7
x= 6     y= 2
x= 9     y= -1
x= 14   y= -2

For non-integer solutions, just pick any x-value other then 4 since then the denominator would be 0 and calculate y=(22-3x)/(x-4). Obviously there are infinite such solutions. If you were to graph it, you would get a hyperbola, which is the points (x,y) present in the solution set of that equation.

Last edited by ShivamS (2014-03-29 04:21:08)