Question

The sum of two number is 18 the sum of their reciprocal is 1 by 4 find the number

Answer 1

Answer: x = 21 , y = -3

Step-by-step explanation:

  let two number be x and y

  x + y = 18

  x = 18 - y.........equation 1

 1/x + 1/y = 1/4

   (y + x)/ xy = 1/4

     4*(y+x) = xy

       4y + 4(18-y) = (18-y)*y     (from equation 1 )

     4y+72-4y = 18y - y^2

          72 = 18y - y^2

         add 9 on both sides

    72+9 = 18y - y^2 +9

81= 2*9*y - y^2 +9

y^2 + 81 - 2*9*y = 9

y^2 +9^2 -2*9*y = 9    (a-b)^2 = a^2 +b^2 -2*a*b)

(y+9)^2 = 3^2

y+9 = 3

y = 3-9

y = -3

put value of y in equation 1

x= 18 - (-3)

x = 21