Question

The sum of two number is 16 and sum of their reciprocals is -1/3 . Find the numbers

Answer 1

Let the 2 numbers be x and y

x + y = 16

(1/x) + (1/y) = 1/3

x = l16 - y

Substitute in the 2nd equation: [1/(16-y)] +(1/y) = 1/3

The common denominator on the left side is y(16-y) and the numerator is y + 16 - y = 16

16/[y(16-y)] = 1/3

This simplifies to y2 - 16y + 48 = 0 which factors as (y-12)(x-4)

The roots are symmetric: if you chose y=12, then x=4 and reverse.

You should check that the solution is correct by plugging into the equation with the fractions!

the common denominator for the left side is y(16-) and the numerator is y + 16 -y = 16

then 16/([y(16-y)] = 1/3 which simplifies to y2 - 16y + 48 = (y-12)(y-4)

the roots are symmetric; if ou choose y = 12, then x = 4 and the reverse

yo

Answer 2

Answer:

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