Question

Sum of two no is 10 and their products is 20...find sum of their reciprocal

Answer 1

let two numbers be x and y

therefore , xy = 20

x + y = 10

x = 10 - y

putting this value above

(10 - y ) × y = 20

y^2 -10y = 20

y^2 -10y + 25 = 20+25

(y - 5 )^2 = 45

taking sq root

y -5 = +/- √45

y-5 = +/- √9×5

y-5 = +/- 3√5

y = 5 +/- 3√5

y = 5 + 3√5 or y = 5 - 3√5

the two numbers are ( 5 + 3√5 and 5 - 3√5 )

sum of their reciprocal ,

= [1/(5 + 3√5)] + [1/ (5 - 3√5)]
= - 1/2