Mister Exam
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Identical expressions
- (x^ two +x+ two)/(x^ two - two x+а^2+6а)= zero
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- x^2+x+2/x^2-2x+а^2+6а=0
- (x^2+x+2)/(x^2-2x+а^2+6а)=O
- (x^2+x+2) divide by (x^2-2x+а^2+6а)=0
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Similar expressions
- (x^2+x+2)/(x^2+2x+а^2+6а)=0
- (x^2+x-2)/(x^2-2x+а^2+6а)=0
- (x^2+x+2)/(x^2-2x-а^2+6а)=0
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- (x^2-x+2)/(x^2-2x+а^2+6а)=0
(x^2+x+2)/(x^2-2x+а^2+6а)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2
x + x + 2
------------------- = 0
2 2
x - 2*x + a + 6*a
$$\frac{x^{2} + x + 2}{a^{2} + 6 a + x^{2} - 2 x} = 0$$
Detail solution
Given the equation:
$$\frac{x^{2} + x + 2}{a^{2} + 6 a + x^{2} - 2 x} = 0$$
Multiply the equation sides by the denominators:
a^2 + x^2 - 2*x + 6*a
we get:
$$\frac{\left(x^{2} + x + 2\right) \left(a^{2} + 6 a + x^{2} - 2 x\right)}{a^{2} + 6 a + x^{2} - 2 x} = 0$$
$$x^{2} + x + 2 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = 2$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{7} i}{2}$$
Simplify
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{7} i}{2}$$
Simplify
$$\frac{x^{2} + x + 2}{a^{2} + 6 a + x^{2} - 2 x} = 0$$
Multiply the equation sides by the denominators:
a^2 + x^2 - 2*x + 6*a
we get:
$$\frac{\left(x^{2} + x + 2\right) \left(a^{2} + 6 a + x^{2} - 2 x\right)}{a^{2} + 6 a + x^{2} - 2 x} = 0$$
$$x^{2} + x + 2 = 0$$
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
$$a = 1$$
$$b = 1$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (2) = -7
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
$$x_{1} = - \frac{1}{2} + \frac{\sqrt{7} i}{2}$$
Simplify
$$x_{2} = - \frac{1}{2} - \frac{\sqrt{7} i}{2}$$
Simplify
The graph
Sum and product of roots
[src]
sum
___ ___
1 I*\/ 7 1 I*\/ 7
0 + - - - ------- + - - + -------
2 2 2 2
$$\left(0 - \left(\frac{1}{2} + \frac{\sqrt{7} i}{2}\right)\right) - \left(\frac{1}{2} - \frac{\sqrt{7} i}{2}\right)$$
=
-1
$$-1$$
product
/ ___\ / ___\ | 1 I*\/ 7 | | 1 I*\/ 7 | 1*|- - - -------|*|- - + -------| \ 2 2 / \ 2 2 /
$$1 \left(- \frac{1}{2} - \frac{\sqrt{7} i}{2}\right) \left(- \frac{1}{2} + \frac{\sqrt{7} i}{2}\right)$$
=
2
$$2$$
2