Question

the sum of two numbers is 8 determine the numbers if the sum of their reciprocal 815​

Answer 1

Let the nos. Be xx and yy.

Let y>xy>x

It is given that y+x=8y+x=8 …(1)

And 1x+1y=8151x+1y=815 …(2)

= y+xxy=815y+xxy=815

From (1)

8xy=8158xy=815

There fore xy=15xy=15 …(3)

Now there are two approches for further calculation

Form a quadrarion by substituting (1) in (3) and finding root. The quadratic will be x2−8x+15=0.x2−8x+15=0. On solving you will get x=3x=3 & 55. And y=5y=5 & 3.3.

This is interpetative method, just think of the no which satisfies both (1) and (3).

Therefore, answers are (3,5) & (5,3).