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Identical expressions
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Similar expressions
- x^2+79^2=159
x^2-79^2=159 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$x^{2} - 79^{2} = 159$$
to
$$\left(x^{2} - 79^{2}\right) - 159 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -6400$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 80$$
Simplify
$$x_{2} = -80$$
Simplify
left part with negative sign.
The equation is transformed from
$$x^{2} - 79^{2} = 159$$
to
$$\left(x^{2} - 79^{2}\right) - 159 = 0$$
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
$$a = 1$$
$$b = 0$$
$$c = -6400$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-6400) = 25600
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 80$$
Simplify
$$x_{2} = -80$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6400$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6400$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6400$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6400$$
Sum and product of roots
[src]
sum
0 - 80 + 80
$$\left(-80 + 0\right) + 80$$
=
0
$$0$$
product
1*-80*80
$$1 \left(-80\right) 80$$
=
-6400
$$-6400$$
-6400
The graph