Question

For every natural number m>1;2m,m²-1and m²+1 form a Pythagoras triplet. Write a program to input the value of'm' through console to display a Pythagoras triplet. Sample Input:3 . Then 2m=6,m²-1=8and m²+1=10. Thus 6,8,10 form a 'Pythagoras Triplet'. Java program only​

Answer 1

Answer:

Let a=m

2

−1

b=2m

c=m

2

+1

using pythagoras theorem, a

2

+b

2

=c

2

So, (m

2

−1)

2

+4m

2

=(m

2

+1)

2

m

4

+1−2m

2

+4m

2

=(m

2

+1)

2

m

4

+2m

2

+1=(m

2

+1)

2

(m

2

+1)

2

=(m

2

+1)

2

Since LHS=RHS , we can say that a,b,c always form pythagorean triplet