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Identical expressions
- nine (x- nine)+ eleven (x- eleven)- two (x- eleven)(x- nine)= zero
- 9(x minus 9) plus 11(x minus 11) minus 2(x minus 11)(x minus 9) equally 0
- nine (x minus nine) plus eleven (x minus eleven) minus two (x minus eleven)(x minus nine) equally zero
- 9x-9+11x-11-2x-11x-9=0
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Similar expressions
- 9(x+9)+11(x-11)-2(x-11)(x-9)=0
- 9(x-9)-11(x-11)-2(x-11)(x-9)=0
- 9(x-9)+11(x-11)+2(x-11)(x-9)=0
- 9(x-9)+11(x-11)-2(x-11)(x+9)=0
- 9(x-9)+11(x+11)-2(x-11)(x-9)=0
- 9(x-9)+11(x-11)-2(x+11)(x-9)=0
9(x-9)+11(x-11)-2(x-11)(x-9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
9*(x - 9) + 11*(x - 11) - 2*(x - 11)*(x - 9) = 0
$$- 2 \left(x - 11\right) \left(x - 9\right) + \left(11 \left(x - 11\right) + 9 \left(x - 9\right)\right) = 0$$
Detail solution
Expand the expression in the equation
$$- 2 \left(x - 11\right) \left(x - 9\right) + \left(11 \left(x - 11\right) + 9 \left(x - 9\right)\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + 60 x - 400 = 0$$
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
$$a = -2$$
$$b = 60$$
$$c = -400$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = 20$$
$$- 2 \left(x - 11\right) \left(x - 9\right) + \left(11 \left(x - 11\right) + 9 \left(x - 9\right)\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + 60 x - 400 = 0$$
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
$$a = -2$$
$$b = 60$$
$$c = -400$$
, then
D = b^2 - 4 * a * c =
(60)^2 - 4 * (-2) * (-400) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = 20$$
Sum and product of roots
[src]
sum
10 + 20
$$10 + 20$$
=
30
$$30$$
product
10*20
$$10 \cdot 20$$
=
200
$$200$$
200