Mister Exam
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2*100+x^2-2*x*(100-1)+1=0 equation
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The solution
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[src]
2 200 + x - 2*x*99 + 1 = 0
$$\left(- 99 \cdot 2 x + \left(x^{2} + 200\right)\right) + 1 = 0$$
Detail solution
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
$$a = 1$$
$$b = -198$$
$$c = 201$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 40 \sqrt{6} + 99$$
$$x_{2} = 99 - 40 \sqrt{6}$$
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
$$a = 1$$
$$b = -198$$
$$c = 201$$
, then
D = b^2 - 4 * a * c =
(-198)^2 - 4 * (1) * (201) = 38400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 40 \sqrt{6} + 99$$
$$x_{2} = 99 - 40 \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -198$$
$$q = \frac{c}{a}$$
$$q = 201$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 198$$
$$x_{1} x_{2} = 201$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -198$$
$$q = \frac{c}{a}$$
$$q = 201$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 198$$
$$x_{1} x_{2} = 201$$
Sum and product of roots
[src]
sum
___ ___ 99 - 40*\/ 6 + 99 + 40*\/ 6
$$\left(99 - 40 \sqrt{6}\right) + \left(40 \sqrt{6} + 99\right)$$
=
198
$$198$$
product
/ ___\ / ___\ \99 - 40*\/ 6 /*\99 + 40*\/ 6 /
$$\left(99 - 40 \sqrt{6}\right) \left(40 \sqrt{6} + 99\right)$$
=
201
$$201$$
201
Rapid solution
[src]
___ x1 = 99 - 40*\/ 6
$$x_{1} = 99 - 40 \sqrt{6}$$
___ x2 = 99 + 40*\/ 6
$$x_{2} = 40 \sqrt{6} + 99$$
x2 = 40*sqrt(6) + 99