Question

the sum of 2 numbers is 40 we need to find the number if of the sum of the reciprocal is 2/5​

Answer 1

Let the numbers be a and b.

a+b = 40, or

b = 40-a …(1)

(1/a)+(1/b) = (2/5), or

5b+5a = 2ab, or

b(2a-5) = 5a or

b = 5a/(2a-5) …(2)

Equate (1) and (2)

40-a = 5a/(2a-5)

(40-a)(2a-5) = 5a

80a-2a^2–200+5a = 5a

2a^2–80a+200 = 0

a^2–40a+100 = 0

a1 = [40 +(1600–400)^0.5]/2

=[40+34.64101615]/2

= 37.32050808

b1 = 40-37.32050808 = 2.67949192

Check: (1/a1)+(1/b1) = (1/37.32050808)+(1/2.67949192) = 0.026794919 + 0.373205081 = 0.4. Correct.

The numbers are 37.32050808 and 2.67949192.