Fill in the blanks :
The solutions of the quadratic equation `x+(1)/(x)=(10)/(3)` are ______ and ______ .

Explanation

`3and(1)/(3),"since",3+(1)/(3)=(10)/(3)and(1)/(3)+(1)/((1)/(3))=(1)/(3)+3=(10)/(3)`
`x+(1)/(x)=(10)/(3)or,(x^(2)+1)/(x)=(10)/(3)or,3x^(2)+3=10x`
or, `3x^(2)-10x+3=0or,3x^(2)-x-9x+3=0`
or, `x(3x-1)-3(3x-1)=0or,(3x-1)(x-3)=0`
`:.3x-1=0or,x=(1)/(3),andx-3=0or,x=3`