Let the required numbers be x and y
Then, ` x + y = 8 " " `… (i)
And, ` (1)/(x)+ (1) /( y) = (8) /( 15) rArr (x + y ) /( xy ) = (8)/( 15)`
` " " rArr ( 8)/(xy ) = (8)/( 15) " " `[using (i) ]
` " " rArr x y = 15 `
`therefore (x - y ) = sqrt (( x+ y ) ^(2) - 4 xy ) `
`" " = sqrt ( 8 ^(2) - 4 xx 15) = sqrt ( 64 - 60) = sqrt 4 = pm 2`.
Thus, we have
`{:(x+ y = 8,,... (i)),(x-y= 2,,... (ii)):}} or {{:(x+ y = 8,,... (iii)),(x-y = - 2,, ... (iv)):}`
On solving (i) and (ii), we get x = 5 and y = 3 .
On solving (iii) and (iv), we get ` x = 3 and y = 5 `.
Hence, the required numbers are 5 and 3 .
