Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 11324*x%=211
-
Equation (x-1)*(x^2+8*x+16)=6*(x+4)
-
Equation x-4/3+x/2=5
-
Equation 7*x^2-28=0
- Express {x} in terms of y where:
- -16*x-2*y=1
- 13*x-13*y=-18
- -2*x+12*y=1
- 8*x-10*y=-13
-
Identical expressions
- eight /(x^ two - eight)= one
- 8 divide by (x squared minus 8) equally 1
- eight divide by (x to the power of two minus eight) equally one
- 8/(x2-8)=1
- 8/x2-8=1
- 8/(x²-8)=1
- 8/(x to the power of 2-8)=1
- 8/x^2-8=1
- 8 divide by (x^2-8)=1
-
Similar expressions
- 8/(x^2+8)=1
8/(x^2-8)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\frac{8}{x^{2} - 8} = 1$$
Multiply the equation sides by the denominators:
-8 + x^2
we get:
$$\frac{8 \left(x^{2} - 8\right)}{x^{2} - 8} = x^{2} - 8$$
$$8 = x^{2} - 8$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$8 = x^{2} - 8$$
to
$$16 - x^{2} = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4$$
$$x_{2} = 4$$
$$\frac{8}{x^{2} - 8} = 1$$
Multiply the equation sides by the denominators:
-8 + x^2
we get:
$$\frac{8 \left(x^{2} - 8\right)}{x^{2} - 8} = x^{2} - 8$$
$$8 = x^{2} - 8$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$8 = x^{2} - 8$$
to
$$16 - x^{2} = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 16$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (16) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4$$
$$x_{2} = 4$$
Sum and product of roots
[src]
sum
-4 + 4
$$-4 + 4$$
=
0
$$0$$
product
-4*4
$$- 16$$
=
-16
$$-16$$
-16
The graph