Short-answer type questions (S.A.) :
(i) Solve : `x+(1)/(x)=(13)/(6)`

Explanation

`x+(1)/(x)=(13)/(6)or,(x^(2)+1)/(x)=(13)/(6)`
or, `6x^(2)+6=13x`
or, `6x^(2)-13x+6=0`
or, `6x^(2)-4x-9x+6=0`
or, `2x(3x-2)-3(3x-2)=0`
or, `(3x-2)(2x-3)=0`
`:.` Either 3x-2=0" " or, 2x-3=0
`implies3x=2" "implies2x=3`
`impliesx=(2)/(3)" "impliesx=(3)/(2)`
`:.` The required solutions are : `impliesx=(2)/(3)andx=(3)/(2)`.