Question

the sum of two number is 16 and the sum of their reciprocal is 1/3find the number

Answer 1

Let the two numbers be x & y

so we get two equations by the condition given in your question

x+y=16. ... (l)

1/x+1/y=1/3

x+y=xy/3

so xy/3=12

xy=48

(x+y)^2=x^2+y^2+2xy

(16)^2=x^2+y^2+2 (48)

256=x^2+y^2+96

x^2+y^2=160

(x-y)^2=x^2+y^2-2xy

(x-y)^2=160-2 (48)

(x-y)^2=64

x-y=8. ... (ll)

by adding equations (l) & (ll) we get

2x=24

x=12

putting x = 12 in equation (ll) we get

12-y=8

y=4

so the number are 12 & 4