Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (|x+4|)=5
-
Equation -2*x-4=3*x
-
Equation x^2+4*x+3=0
-
Equation x^4-2*x^3+x^2-1=0
- Express {x} in terms of y where:
- 6*x-19*y=-18
- 15*x+1*y=19
- -2*x+2*y=4
- 10*x+3*y=2
-
Identical expressions
- one /x^ two + two /x- three = zero
- 1 divide by x squared plus 2 divide by x minus 3 equally 0
- one divide by x to the power of two plus two divide by x minus three equally zero
- 1/x2+2/x-3=0
- 1/x²+2/x-3=0
- 1/x to the power of 2+2/x-3=0
- 1/x^2+2/x-3=O
- 1 divide by x^2+2 divide by x-3=0
-
Similar expressions
- 1/x^2-2/x-3=0
- 1/x^2+2/x+3=0
1/x^2+2/x-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1 2 -- + - - 3 = 0 2 x x
$$\left(\frac{1}{x^{2}} + \frac{2}{x}\right) - 3 = 0$$
Detail solution
Given the equation:
$$\left(\frac{1}{x^{2}} + \frac{2}{x}\right) - 3 = 0$$
Multiply the equation sides by the denominators:
x^2
we get:
$$x^{2} \left(\left(\frac{1}{x^{2}} + \frac{2}{x}\right) - 3\right) = 0$$
$$- 3 x^{2} + 2 x + 1 = 0$$
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
$$a = -3$$
$$b = 2$$
$$c = 1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{3}$$
$$x_{2} = 1$$
$$\left(\frac{1}{x^{2}} + \frac{2}{x}\right) - 3 = 0$$
Multiply the equation sides by the denominators:
x^2
we get:
$$x^{2} \left(\left(\frac{1}{x^{2}} + \frac{2}{x}\right) - 3\right) = 0$$
$$- 3 x^{2} + 2 x + 1 = 0$$
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
$$a = -3$$
$$b = 2$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (-3) * (1) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{3}$$
$$x_{2} = 1$$
Sum and product of roots
[src]
sum
1 - 1/3
$$- \frac{1}{3} + 1$$
=
2/3
$$\frac{2}{3}$$
product
-1/3
$$- \frac{1}{3}$$
=
-1/3
$$- \frac{1}{3}$$
-1/3
The graph