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Two positive integers a and b are such that a + b = a/b + b/a . What is the value of a 2 + b 2 ?

Two positive integers a and b are such that a+b = a/b + b/a. What is the value of a2 +b2? 

Grade:9

2 Answers

Arun
25750 Points
6 years ago
this is only valid if a = 1 and b = 1hence put a
Sriyansh Dash
26 Points
5 years ago
a+b=a/b+b/a
=a+b=a^2+b^2/ab
=a^2b+b^2a=a^2+b^2
Comparing both sides we get ,
a^2b=a^2
=b=1
 
b^2a=b^2
=a=1

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