Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-8*x+17=0
- Equation x^2-y^2=0
-
Equation x+19=12
-
Equation 4*(x-3)=x+6
- Express {x} in terms of y where:
- 7*x+19*y=12
- 11*x-20*y=-10
- 18*x-11*y=2
- -7*x-13*y=5
- Canonical form:
-
x^2-y^2
- Inequation:
- x^2-y^2
- Factor polynomial:
- x^2-y^2
-
Identical expressions
- x^ two -y^ two = zero
- x squared minus y squared equally 0
- x to the power of two minus y to the power of two equally zero
- x2-y2=0
- x²-y²=0
- x to the power of 2-y to the power of 2=0
- x^2-y^2=O
-
Similar expressions
- x^2+y^2=0
x^2-y^2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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
$$a = 1$$
$$b = 0$$
$$c = - y^{2}$$
, then
The equation has two roots.
or
$$x_{1} = \sqrt{y^{2}}$$
$$x_{2} = - \sqrt{y^{2}}$$
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
$$a = 1$$
$$b = 0$$
$$c = - y^{2}$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-y^2) = 4*y^2
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{y^{2}}$$
$$x_{2} = - \sqrt{y^{2}}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - y^{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - y^{2}$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - y^{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - y^{2}$$
The graph
Sum and product of roots
[src]
sum
-re(y) - I*im(y) + I*im(y) + re(y)
$$\left(- \operatorname{re}{\left(y\right)} - i \operatorname{im}{\left(y\right)}\right) + \left(\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)}\right)$$
=
0
$$0$$
product
(-re(y) - I*im(y))*(I*im(y) + re(y))
$$\left(- \operatorname{re}{\left(y\right)} - i \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)}\right)$$
=
2 -(I*im(y) + re(y))
$$- \left(\operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)}\right)^{2}$$
-(i*im(y) + re(y))^2
Rapid solution
[src]
x1 = -re(y) - I*im(y)
$$x_{1} = - \operatorname{re}{\left(y\right)} - i \operatorname{im}{\left(y\right)}$$
x2 = I*im(y) + re(y)
$$x_{2} = \operatorname{re}{\left(y\right)} + i \operatorname{im}{\left(y\right)}$$
x2 = re(y) + i*im(y)