the number is 5 or 1
let x-- be the number
then 1/x be the reciprocal of the number.
then the equation will be-->x+5(1/x)=6
x+5/x=6
x(x+5/x=6)x (to eliminate the x as the denominator of 5)
x^2+5=6x
X^2-6x+5=0
by quadratic equation -b+-(plus and minus) the square root of b^2-4ac all over 2a
= -(-6)+-(plus and minus) the square root of 36-4(1)(5) all over 2
= 6+-(plus and minus) the square root of 36-20 all over 2
= 6+-(plus and minus) the square root of 16 all over 2
= 6+-(plus and minus) 4 all over 2
= 5 or 1 :D