Question

If p is a positive integer, then 3p+25/2p-5 can be a positive integer if and only if p is ______​

Answer 1

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Answer 2

Answer:

p is a positive integer.

2p−5

3p+25

​  

 is also a positive integer.

(3p+25)(2p-5)>0

2p-5>0  [∵ 3p+25 is always >0]

p>  

2

5

​  

 

As p is an integer,  

∴ p≥3

2p−5

3p+25

​  

=1+  

2p−5

p+30

​  

 

For  

2p−5

3p+25

​  

 to be an integer,

Minimum of  

2p−5

p+30

​  

=1

p+30 = 2p-5  

p = 35

p = 35 is the maximum possible value of p.

∴pϵ(3,35)

Step-by-step explanation: