Question

If xPlus 1/x is equalto 17/4 then find the value of x

Answer 1

Answer:

$x + \frac{1}{x} = \frac{17}{4} \\ = \frac{ {x}^{2} + 1}{x} = \frac{17}{4} \\ cross \: multiplcation \\ = 4( {x}^{2} + 1) = 17x \\ = 4 {x}^{2} + 4 = 17x \\ 4 {x}^{2} - 17x + 4 = 0 \\ 4 {x}^{2} - 16x - x + 4 = 0 \\ 4x(x - 4) - 1(x - 4) \\ =( 4x - 1)(x - 4) \\ x = \frac{1}{4} \: o r \: x = 4$