Question

the sum of two numbers is 18 the sum of their reciprocal is 1 upon 4 find the numbers ​

Answer 1

Answer:

let the first no. be X and second be Y

Now, According to question

$x + y = 18$

equation 1

1/X+1/y=1/4

equation 2

from equation1

$x = 18 - y$

putting in equation 2

1/18-y +1/y. =1/4

taking LCM

y+18-y/(18-y)y =1/4

18/18y-y^2 =1/4

$72 = 18y - y {2}$

$72 - 18y + y {2} = 0$

$y {2} - 18y + 72 = 0$

$y {2} - 6y - 12y + 72$

$y(y - 6) - 12(y - 6)$

$(y - 6)(y - 12)$

y=6,12

putting in equation 1

$x + y = 18$

$x + 6 = 18$

$x = 12$

OR

$x + 12 = 18$

$x = 6$

X=12,6

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