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- Equation:
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Equation x^2-9x+20=0
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Equation 1/(x-1)^2+4/(x-1)-12=0
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Equation x^2-2x-24=0
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Equation 5x^2-15x=0
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Identical expressions
- one /(x- one)^ two + four /(x- one)- twelve = zero
- 1 divide by (x minus 1) squared plus 4 divide by (x minus 1) minus 12 equally 0
- one divide by (x minus one) to the power of two plus four divide by (x minus one) minus twelve equally zero
- 1/(x-1)2+4/(x-1)-12=0
- 1/x-12+4/x-1-12=0
- 1/(x-1)²+4/(x-1)-12=0
- 1/(x-1) to the power of 2+4/(x-1)-12=0
- 1/x-1^2+4/x-1-12=0
- 1/(x-1)^2+4/(x-1)-12=O
- 1 divide by (x-1)^2+4 divide by (x-1)-12=0
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Similar expressions
- 1/(x-1)^2+4/(x+1)-12=0
- 1/(x+1)^2+4/(x-1)-12=0
- 1/(x-1)^2-4/(x-1)-12=0
- 1/(x-1)^2+4/(x-1)+12=0
1/(x-1)^2+4/(x-1)-12=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
1 4
-------- + ----- - 12 = 0
2 x - 1
(x - 1)
$$\left(\frac{1}{\left(x - 1\right)^{2}} + \frac{4}{x - 1}\right) - 12 = 0$$
Detail solution
Given the equation:
$$\left(\frac{1}{\left(x - 1\right)^{2}} + \frac{4}{x - 1}\right) - 12 = 0$$
Multiply the equation sides by the denominators:
(-1 + x)^2
we get:
$$\left(x - 1\right)^{2} \left(\left(\frac{1}{\left(x - 1\right)^{2}} + \frac{4}{x - 1}\right) - 12\right) = 0$$
$$- 12 x^{2} + 28 x - 15 = 0$$
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
$$a = -12$$
$$b = 28$$
$$c = -15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{6}$$
$$x_{2} = \frac{3}{2}$$
$$\left(\frac{1}{\left(x - 1\right)^{2}} + \frac{4}{x - 1}\right) - 12 = 0$$
Multiply the equation sides by the denominators:
(-1 + x)^2
we get:
$$\left(x - 1\right)^{2} \left(\left(\frac{1}{\left(x - 1\right)^{2}} + \frac{4}{x - 1}\right) - 12\right) = 0$$
$$- 12 x^{2} + 28 x - 15 = 0$$
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
$$a = -12$$
$$b = 28$$
$$c = -15$$
, then
D = b^2 - 4 * a * c =
(28)^2 - 4 * (-12) * (-15) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{6}$$
$$x_{2} = \frac{3}{2}$$
Sum and product of roots
[src]
sum
5/6 + 3/2
$$\frac{5}{6} + \frac{3}{2}$$
=
7/3
$$\frac{7}{3}$$
product
5*3 --- 6*2
$$\frac{3 \cdot 5}{2 \cdot 6}$$
=
5/4
$$\frac{5}{4}$$
5/4
The graph