If The sum of 2 numbers is 25 and sum of their reciprocals is 0.25 then what are the numbers?

Answer 1

x+y=251/x + 1/y=.25

Solve for y in both:

y=25-x

1/y=.25-1/x, so y=1/(.25-1/x)

Use substitution:

25-x=1/(.25-1/x)

(25-x)(.25-1/x)=1

6.25-25/x -.25x+1=1

Combine like terms:

-.25x+6.25-25/x=0

Multiply everything by x:

-.25x^2 +6.25x-25=0

Multiply everything by negative 1:

.25x^2-6.25x+25=0

Multiply everything by 4:

x^2 -25x +100=0

Use the quadratic formula:

x=[25±√(25^2 -4(1)(100)]/2(1)

x=[25±√(625-400)]/2

x=[25±√225]/2

x=(25±15)/2

x=40/2 or x=10/2

x=20 or x=5

Plug these values into the original equation, and you will see that y also = 20 or 5.

So, the two pairs of numbers that satisfy the original equation are:

x=5, y=20; and x=20, y=5