+0  
 
0
212
1
avatar

x= 4-x/y^2-x 

 

How many ordered pairs of positive integers (x,y) satisfy the equation above. 

 

Multiple Choice answers

 

a) 0

b) 1

c) 2

d) 3

e) 4

Guest Jan 2, 2018
 #1
avatar+87621 
+1

x =  (4 - x) / (y^2 - x)

 

y^2x  - x^2  =   4 - x

 

y^2x  =   x^2 - x  +   4

 

y^2  =   [ x^2  -  x  +  4 ]  /  x

 

y^2  =  x  -  1   +  4/x

 

Notice  that  the first two terms always result in an integer for any integer value of x

 

But   4/x     is only an integer  when x  =  ±1, ±2 or ±4

 

But we can reject  the negative values  because  they make the right side negative.....so y is not a real number  for these values

 

And when x = 2,  y  = ±√3    which isn't an integer pair

 

So.....when  x  =  1,  y   = ±2

And when  x  =   4,  y   = ±2

 

So......the ordered pairs of positive integers that make this true  are  (1,2), (-1,2), (4, 2)  and (4 , -2)

 

So....the correct answer is  (e)

 

 

 

 

cool cool cool

CPhill  Jan 2, 2018
edited by CPhill  Jan 3, 2018

16 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.