Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/4+13=x+1
-
Equation 4(x-8)=-5
-
Equation 3x-2=0
-
Equation x*8=25+15
- Express {x} in terms of y where:
- 4*x+8*y=7
- -14*x+5*y=3
- 13*x-18*y=-17
- 4*x+18*y=-7
- Graphing y =:
- (x^2-x+1)/(x-1)
- Derivative of:
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(x^2-x+1)/(x-1)
-
Identical expressions
- (x^ two -x+ one)/(x- one)= zero
- (x squared minus x plus 1) divide by (x minus 1) equally 0
- (x to the power of two minus x plus one) divide by (x minus one) equally zero
- (x2-x+1)/(x-1)=0
- x2-x+1/x-1=0
- (x²-x+1)/(x-1)=0
- (x to the power of 2-x+1)/(x-1)=0
- x^2-x+1/x-1=0
- (x^2-x+1)/(x-1)=O
- (x^2-x+1) divide by (x-1)=0
-
Similar expressions
- (x^2+x+1)/(x-1)=0
- (x^2-x+1)/(x+1)=0
- (x^2-x-1)/(x-1)=0
(x^2-x+1)/(x-1)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 x - x + 1 ---------- = 0 x - 1
$$\frac{\left(x^{2} - x\right) + 1}{x - 1} = 0$$
Detail solution
Given the equation:
$$\frac{\left(x^{2} - x\right) + 1}{x - 1} = 0$$
Multiply the equation sides by the denominators:
-1 + x
we get:
$$\frac{\left(x - 1\right) \left(\left(x^{2} - x\right) + 1\right)}{x - 1} = 0$$
$$x^{2} - x + 1 = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{1}{2} + \frac{\sqrt{3} i}{2}$$
$$x_{2} = \frac{1}{2} - \frac{\sqrt{3} i}{2}$$
$$\frac{\left(x^{2} - x\right) + 1}{x - 1} = 0$$
Multiply the equation sides by the denominators:
-1 + x
we get:
$$\frac{\left(x - 1\right) \left(\left(x^{2} - x\right) + 1\right)}{x - 1} = 0$$
$$x^{2} - x + 1 = 0$$
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
$$a = 1$$
$$b = -1$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (1) = -3
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2} + \frac{\sqrt{3} i}{2}$$
$$x_{2} = \frac{1}{2} - \frac{\sqrt{3} i}{2}$$
Sum and product of roots
[src]
sum
___ ___ 1 I*\/ 3 1 I*\/ 3 - - ------- + - + ------- 2 2 2 2
$$\left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right) + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)$$
=
1
$$1$$
product
/ ___\ / ___\ |1 I*\/ 3 | |1 I*\/ 3 | |- - -------|*|- + -------| \2 2 / \2 2 /
$$\left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)$$
=
1
$$1$$
1
Rapid solution
[src]
___
1 I*\/ 3
x1 = - - -------
2 2
$$x_{1} = \frac{1}{2} - \frac{\sqrt{3} i}{2}$$
___
1 I*\/ 3
x2 = - + -------
2 2
$$x_{2} = \frac{1}{2} + \frac{\sqrt{3} i}{2}$$
x2 = 1/2 + sqrt(3)*i/2
Numerical answer
[src]
x1 = 0.5 - 0.866025403784439*i
x2 = 0.5 + 0.866025403784439*i
x2 = 0.5 + 0.866025403784439*i
The graph