Question

If (1/x-1/y) varises(1/x-y) then show that (x^2+y^2) varises xy​

Answer 1

Step-by-step explanation:

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

.......hope it helped you......

Answer 2

Step-by-step explanation:

1/y-1/x propto1/x-y; Or(x-y)/xy=k*1/(x-y)(where k ne0); Or * (x - y) ^ 2 = kxy; Or x^ 2 -2xy^ + y^ 2 =kxyOr x ^ 2 + y ^ 2 = (k + 2) * x * y; Or * (x ^ 2 + y ^ 2) / x * y = k + 2 Or x / y + y / x = k + 2; Or * (x / y) ^ 2 + 1 = c(x / y) (where c = k + 2 = c constant) Or * (x / y) ^ 2 - 2(x / y) * (c / 2) + c ^ 2 / 4 + 1 - c / 4 = 0; Or * (x / y - c / 2) ^ 2 = (c ^ 2 / 4) - 1 Or x/y-c/2= pm sqrt (c^ 2 -4)/2 Or x/y=(c/2) pm sqrt (c^ 2 -4)/2 Or x/y=constant