Question

Find the roots of the quadratic equation X- 1/3x = 1/6​

Answer 1

Hey Mate

Hey Mate roots of the equation are 2/3 , -1/2

Step-by-step explanation:

$x - \frac{1}{3x} = \frac{1}{6} \\ \\ \frac{3 {x}^{2} - 1}{3 x} = \frac{1}{6} \\ \\ 2(3 {x}^{2} - 1) = 1 \times x \\ \\ 6 {x}^{2} - 2 = x \\ 6 {x}^{2} - x - 2 = 0 \\ \\ 6 {x}^{2} - 4x + 3x - 2 = 0 \\ \\ 2x(3x - 2) + 1(3x - 2) = 0 \\ \\ (3x - 2)(2x + 1) = 0$

Answer 2

$x - \frac{1}{3x} = \frac{1}{6} \\ \\ (taking \: lcm \: ) \\ \frac{3 {x}^{2} - 1 }{3x} = \frac{1}{6} \\ \\ (cross \: multiplying) \\ 18 {x}^{2} - 6 = 3x \\ \\ 18 {x}^{2} - 3x - 6 = 0 \\ \\ (dividing \: by \: 3 \: both \: sides) \\ 6 {x}^{2} - x - 2 = 0 \\ \\ 6 {x}^{2} - x(4 - 3) - 2 = 0 \\ \\ 6 {x}^{2} - 4x + 3x - 2 = 0 \\ \\ 2x(3x - 2) + 1(3x - 2) = 0 \\ \\ (2x + 1)(3x - 2) = 0 \\ \\ \\ \\ so \: the \: two \: roots \: of \: eqn \: are \: \\ x = \frac{ - 1}{2} \\ and \\ x = \frac{2}{3}$