Question

If H.C.F (a, b) = 1 then

is in ___________ terms.If H.C.F (a, b) = 1 then

is in ___________ terms.

Answer 1

Step-by-step explanation:

Suppose the HCF of (x−y,x+y) is m.

∴

x−y

m

and

x+y

m

∴ a−b=am and a+b=bm

∴ 2x=(a+b)m

Also 2y=(b−a)m

Now HCF of (x,y)=1

∴ 2 HCF of (x,y)=2

HCF of ((a+b)m,(b−a)m) is 2

m× HCF of (a+b,b−a)=2×1=2

∴ m=1 or 2.