Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation x^4-4*x^3-2*x^2+12*x+9=0
-
Equation sin(x)=-1
-
Equation cos(x)=sqrt(3)/2
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 1*x-6*y=-19
- -19*x-14*y=-8
- 9*x-4*y=2
-
Identical expressions
- ((two *(x^ two + six x+ eight)-(x^ two -5x-6))/(x^ two +3x+ two))- forty-one = zero
- ((2 multiply by (x squared plus 6x plus 8) minus (x squared minus 5x minus 6)) divide by (x squared plus 3x plus 2)) minus 41 equally 0
- ((two multiply by (x to the power of two plus six x plus eight) minus (x to the power of two minus 5x minus 6)) divide by (x to the power of two plus 3x plus two)) minus forty minus one equally zero
- ((2*(x2+6x+8)-(x2-5x-6))/(x2+3x+2))-41=0
- 2*x2+6x+8-x2-5x-6/x2+3x+2-41=0
- ((2*(x²+6x+8)-(x²-5x-6))/(x²+3x+2))-41=0
- ((2*(x to the power of 2+6x+8)-(x to the power of 2-5x-6))/(x to the power of 2+3x+2))-41=0
- ((2(x^2+6x+8)-(x^2-5x-6))/(x^2+3x+2))-41=0
- ((2(x2+6x+8)-(x2-5x-6))/(x2+3x+2))-41=0
- 2x2+6x+8-x2-5x-6/x2+3x+2-41=0
- 2x^2+6x+8-x^2-5x-6/x^2+3x+2-41=0
- ((2*(x^2+6x+8)-(x^2-5x-6))/(x^2+3x+2))-41=O
- ((2*(x^2+6x+8)-(x^2-5x-6)) divide by (x^2+3x+2))-41=0
-
Similar expressions
- ((2*(x^2+6x-8)-(x^2-5x-6))/(x^2+3x+2))-41=0
- ((2*(x^2+6x+8)-(x^2-5x-6))/(x^2-3x+2))-41=0
- ((2*(x^2+6x+8)+(x^2-5x-6))/(x^2+3x+2))-41=0
- ((2*(x^2+6x+8)-(x^2+5x-6))/(x^2+3x+2))-41=0
- ((2*(x^2-6x+8)-(x^2-5x-6))/(x^2+3x+2))-41=0
- ((2*(x^2+6x+8)-(x^2-5x-6))/(x^2+3x+2))+41=0
- ((2*(x^2+6x+8)-(x^2-5x+6))/(x^2+3x+2))-41=0
- ((2*(x^2+6x+8)-(x^2-5x-6))/(x^2+3x-2))-41=0
((2*(x^2+6x+8)-(x^2-5x-6))/(x^2+3x+2))-41=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 2 \ 2
2*\x + 6*x + 8/ + - x + 5*x + 6
--------------------------------- - 41 = 0
2
x + 3*x + 2
$$-41 + \frac{\left(\left(- x^{2} + 5 x\right) + 6\right) + 2 \left(\left(x^{2} + 6 x\right) + 8\right)}{\left(x^{2} + 3 x\right) + 2} = 0$$
Detail solution
Given the equation:
$$-41 + \frac{\left(\left(- x^{2} + 5 x\right) + 6\right) + 2 \left(\left(x^{2} + 6 x\right) + 8\right)}{\left(x^{2} + 3 x\right) + 2} = 0$$
Multiply the equation sides by the denominators:
2 + x^2 + 3*x
we get:
$$\left(-41 + \frac{\left(\left(- x^{2} + 5 x\right) + 6\right) + 2 \left(\left(x^{2} + 6 x\right) + 8\right)}{\left(x^{2} + 3 x\right) + 2}\right) \left(x^{2} + 3 x + 2\right) = 0$$
$$- 40 x^{2} - 106 x - 60 = 0$$
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
$$a = -40$$
$$b = -106$$
$$c = -60$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{53}{40} - \frac{\sqrt{409}}{40}$$
$$x_{2} = - \frac{53}{40} + \frac{\sqrt{409}}{40}$$
$$-41 + \frac{\left(\left(- x^{2} + 5 x\right) + 6\right) + 2 \left(\left(x^{2} + 6 x\right) + 8\right)}{\left(x^{2} + 3 x\right) + 2} = 0$$
Multiply the equation sides by the denominators:
2 + x^2 + 3*x
we get:
$$\left(-41 + \frac{\left(\left(- x^{2} + 5 x\right) + 6\right) + 2 \left(\left(x^{2} + 6 x\right) + 8\right)}{\left(x^{2} + 3 x\right) + 2}\right) \left(x^{2} + 3 x + 2\right) = 0$$
$$- 40 x^{2} - 106 x - 60 = 0$$
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
$$a = -40$$
$$b = -106$$
$$c = -60$$
, then
D = b^2 - 4 * a * c =
(-106)^2 - 4 * (-40) * (-60) = 1636
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{53}{40} - \frac{\sqrt{409}}{40}$$
$$x_{2} = - \frac{53}{40} + \frac{\sqrt{409}}{40}$$
Rapid solution
[src]
_____
53 \/ 409
x1 = - -- - -------
40 40
$$x_{1} = - \frac{53}{40} - \frac{\sqrt{409}}{40}$$
_____
53 \/ 409
x2 = - -- + -------
40 40
$$x_{2} = - \frac{53}{40} + \frac{\sqrt{409}}{40}$$
x2 = -53/40 + sqrt(409)/40
Sum and product of roots
[src]
sum
_____ _____ 53 \/ 409 53 \/ 409 - -- - ------- + - -- + ------- 40 40 40 40
$$\left(- \frac{53}{40} - \frac{\sqrt{409}}{40}\right) + \left(- \frac{53}{40} + \frac{\sqrt{409}}{40}\right)$$
=
-53 ---- 20
$$- \frac{53}{20}$$
product
/ _____\ / _____\ | 53 \/ 409 | | 53 \/ 409 | |- -- - -------|*|- -- + -------| \ 40 40 / \ 40 40 /
$$\left(- \frac{53}{40} - \frac{\sqrt{409}}{40}\right) \left(- \frac{53}{40} + \frac{\sqrt{409}}{40}\right)$$
=
3/2
$$\frac{3}{2}$$
3/2