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Plz help to solve the question. 
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Asked by adilaman.java | 08 Feb, 2019, 05:59: PM
answered-by-expert Expert Answer
( n2+1 )/2  >  ( n2-1 )/2 > n
 
hence we consider ( n2+1 )/2 is hypotenuse and other two numbers are sides of right angles.
 
begin mathsize 12px style open parentheses n squared space plus space 1 close parentheses squared over 4 space equals space fraction numerator begin display style open parentheses n squared space minus space 1 close parentheses squared end style begin display style space end style begin display style plus end style begin display style space end style begin display style 4 end style begin display style begin display style n end style squared end style over denominator 4 end fraction space equals space open parentheses fraction numerator n squared minus 1 over denominator 2 end fraction close parentheses squared space plus space n squared end style
hence begin mathsize 12px style open parentheses fraction numerator n squared plus 1 over denominator 2 end fraction space comma space fraction numerator n squared minus 1 over denominator 2 end fraction comma space n squared close parentheses space end style is a pythagorean triplet.
let n= 3, then  applying the above relations, we have (5,4,3) is  a pythagorean triplet
let n = 5, then  applying the above relations, we have (13,12,5) is  a pythagorean triplet
Answered by Thiyagarajan K | 10 Feb, 2019, 01:31: PM

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