The sum of a number and its reciprocal is `(10)/(3)`, find the number(s).

Explanation

Let the number be x
:. According to given statement
`x+(1)/(x)=(10)/(3)`
`implies(x^(2+1))/(x)=(10)/(3)`
`implies3x^(2)+3=10x`
`implies3x^(2)-10x+3=0`
`implies3x^(2)-(9+1)x+3=0`
`implies3x^(2)-9x-x+3=0`
`implies3x(x-3)-1(x-3)=0`
`implies(3x-1)(x-3)=0`
when `3x-1=0," "x=(1)/(3)`
and when x-3=0, x=3
Hence, the number (s) are 3 and (1)/(3).