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ques:- A,B,C are 3 distinct integers and (1/A+1/B+1/C) IS ALSO AN INTEGER. FIND THE VALUE OF A,B,C.

ques:- A,B,C are 3 distinct integers and (1/A+1/B+1/C) IS ALSO AN INTEGER. FIND THE VALUE OF A,B,C.

Grade:11

2 Answers

Askiitian.Expert Rajat
24 Points
12 years ago

Hi ANIRUDDHO

 

Since ABC are distinct, therefore possible values of ABC are:

(-n n 1) and (-n n -1)

where n is any non zero integer

the order for ABC can be anything but the triplets have to be of this form

Reasons:

 

If a;ll are distinct and posiotive, it(1/A+1/B+1/C) would not be an integer

If a;ll are distinct and negative, it(1/A+1/B+1/C) would not be an integer

Henxce the form given is obtained

 

Regards

Rajat

mycroft holmes
272 Points
12 years ago

well you can have A,B, C +ve and still have 1/A  + 1/B +  1/C an integer. e.g. A =2, B=3, C=6

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