Question

If m is natural number greater than 1,then 2m,m²-1, and m²+1 always from a Pythagorean triplet with (2m)²+(m²-1)²=(m²+1)²

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.