Question

If 1/x+1/y ∝1/x+y, then prove that (x+y)∝(x-y)​

Answer 1

Answer:

1/y-1/x∝1/x-y

Or (x-y)/xy=k×1/(x-y)(where k≠0)

Or (x-y)²=kxy

Or x²-2xy+y²=kxy

Or x²+y²=(k+2)xy

Or (x²+y²)/xy=k+2

Or x/y+y/x=k+2

Or (x/y)²+1=c(x/y) (where c=k+2 =constant)

Or (x/y)²-2(x/y)(c/2)+c²/4+1-c/4=0

Or (x/y-c/2)²=(c²/4)–1

Or x/y-c/2=±√(c²-4)/2

Or x/y=(c/2)±√(c²-4)/2

Or x/y=constant

Therefore x∝y

Step-by-step explanation:

it is with step