Question

In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`

Answer 1

`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`.
`(x^2 + 1)/x = (13)/(6)`
⇒ 6x² - 12x + 6 = 0
Now on substitute x = `(5)/(6)` in equation
L.H.S. = `6 xx (5/6)^2 - 13 xx (5)/(6) + 6`
⇒ = `(25)/(6) - (65)/(6) + 6`
⇒ = `(61)/(6) - (65)/(6) ≠ 0 ≠ "R.H.S."`
∴ x = `(5)/(6)` is not a solution of the given equation.
on substituting x = `(4)/(3)` in L.H.S. of given equation
⇒ L.H.S. = `6 xx (4/3)^2 - 13 xx (4)/(3) + 6`
= `(32)/(3) - (52)/(3) + 6`
= `(50)/(3) - (52)/(3) ≠ 0 ≠ "R.H.S."`
Hence, `(4)/(3)` is not a solution of the given equation.