Question

if 3x^2 +4x-3=0,then x-1/x will be​

Answer 1

Answer:

The value of $x-\frac{1}{x}$ is -1.33.

Step-by-step explanation:

The equation provided is: $3x^{2}+4x-3=0$

The equation is a quadratic equation.

The roots of a quadratic equation are:$x=\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

Here a = 3, b = 4 and c = -3.

The roots are:

$x=\frac{-4\pm\sqrt{4^{2}-(4\times3\times-3)} }{2\times3}\\=\frac{-4\pm\sqrt{52} }{6}\\=\frac{-4\pm2\sqrt{13} }{6}\\ =\frac{-2\pm\sqrt{13} }{3}$

• If $x=\frac{-2-\sqrt{13} }{3}$ the value of $x-\frac{1}{x}$ is:

                  $x-\frac{1}{x}=\frac{-2-\sqrt{13} }{3}-\frac{3}{-2-\sqrt{13} }\\ =\frac{(-2-\sqrt{13})^{2}-9 }{-6-3\sqrt{13} }\\\approx-1.33$

• If $x=\frac{-2+\sqrt{13} }{3}$the value of $x-\frac{1}{x}$ is:

                  $x-\frac{1}{x}=\frac{-2+\sqrt{13} }{3}-\frac{3}{-2+\sqrt{13} }\\ =\frac{(-2+\sqrt{13})^{2}-9 }{-6+3\sqrt{13} }\\\approx-1.33$

Thus, the value of $x-\frac{1}{x}$ is -1.33.