Question

If 1/x +1/y=1/x and xy=20/1 then what is the average of x and y? please explain​

Answer 1

Answer=The R.H.S. of the equation is a sequence in geometric progression with infinite terms, with,

first term, i.e., a = x, and

common ratio, i.e., r = -x

Now, sum of a sequence in geometric progression with infinite terms is given by

S = a/(1-r)

Here, x∈(-1, 1], otherwise the sum of the terms will be infinite.

Therefore,

R.H.S. = x/(1+x)

Now, y = x/(1+x)

⇒ y+xy = x

⇒ y = x(1-y)

⇒ x = y/(1-y) = answer

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