Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 1/x^2-1/x-6=0
-
Equation x^2-8=0
-
Equation x^2=-3
-
Equation x^4-2*x^3+x^2-1=0
- Express {x} in terms of y where:
- -9*x-12*y=-19
- 6*x+7*y=-10
- 4*x-11*y=-2
- -5*x-2*y=-14
-
Identical expressions
- one /x^ two - one /x- six = zero
- 1 divide by x squared minus 1 divide by x minus 6 equally 0
- one divide by x to the power of two minus one divide by x minus six equally zero
- 1/x2-1/x-6=0
- 1/x²-1/x-6=0
- 1/x to the power of 2-1/x-6=0
- 1/x^2-1/x-6=O
- 1 divide by x^2-1 divide by x-6=0
-
Similar expressions
- 1/x^2+1/x-6=0
- 1/x^2-1/x+6=0
1/x^2-1/x-6=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 1 -- - - - 6 = 0 2 x x
$$\left(\frac{1}{x^{2}} - \frac{1}{x}\right) - 6 = 0$$
Detail solution
Given the equation:
$$\left(\frac{1}{x^{2}} - \frac{1}{x}\right) - 6 = 0$$
Multiply the equation sides by the denominators:
x^2
we get:
$$x^{2} \left(\left(\frac{1}{x^{2}} - \frac{1}{x}\right) - 6\right) = 0$$
$$- 6 x^{2} - x + 1 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -6$$
$$b = -1$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{3}$$
$$\left(\frac{1}{x^{2}} - \frac{1}{x}\right) - 6 = 0$$
Multiply the equation sides by the denominators:
x^2
we get:
$$x^{2} \left(\left(\frac{1}{x^{2}} - \frac{1}{x}\right) - 6\right) = 0$$
$$- 6 x^{2} - x + 1 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = -6$$
$$b = -1$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (-6) * (1) = 25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{3}$$
Sum and product of roots
[src]
sum
-1/2 + 1/3
$$- \frac{1}{2} + \frac{1}{3}$$
=
-1/6
$$- \frac{1}{6}$$
product
-1 --- 2*3
$$- \frac{1}{6}$$
=
-1/6
$$- \frac{1}{6}$$
-1/6
The graph