Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x+y=15
-
Equation 3*x=12
-
Equation 4,3x-3,5=2,5x+1,9
-
Equation sin(x)=5/2
- Express {x} in terms of y where:
- -12*x+10*y=2
- -6*x+20*y=-18
- 19*x-7*y=10
- 14*x+3*y=-1
- Canonical form:
- (x-1)^2
- Graphing y =:
- (x-1)^2
- Derivative of:
-
(x-1)^2
-
Identical expressions
- (x- one)^ two = three
- (x minus 1) squared equally 3
- (x minus one) to the power of two equally three
- (x-1)2=3
- x-12=3
- (x-1)²=3
- (x-1) to the power of 2=3
- x-1^2=3
-
Similar expressions
- (x+1)^2=3
(x-1)^2=3 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
$$\left(x - 1\right)^{2} = 3$$
to
$$\left(x - 1\right)^{2} - 3 = 0$$
Expand the expression in the equation
$$\left(x - 1\right)^{2} - 3 = 0$$
We get the quadratic equation
$$x^{2} - 2 x - 2 = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1 + \sqrt{3}$$
$$x_{2} = 1 - \sqrt{3}$$
left part with negative sign.
The equation is transformed from
$$\left(x - 1\right)^{2} = 3$$
to
$$\left(x - 1\right)^{2} - 3 = 0$$
Expand the expression in the equation
$$\left(x - 1\right)^{2} - 3 = 0$$
We get the quadratic equation
$$x^{2} - 2 x - 2 = 0$$
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
$$a = 1$$
$$b = -2$$
$$c = -2$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-2) = 12
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1 + \sqrt{3}$$
$$x_{2} = 1 - \sqrt{3}$$
Sum and product of roots
[src]
sum
___ ___ 1 - \/ 3 + 1 + \/ 3
$$\left(1 - \sqrt{3}\right) + \left(1 + \sqrt{3}\right)$$
=
2
$$2$$
product
/ ___\ / ___\ \1 - \/ 3 /*\1 + \/ 3 /
$$\left(1 - \sqrt{3}\right) \left(1 + \sqrt{3}\right)$$
=
-2
$$-2$$
-2
Rapid solution
[src]
___ x1 = 1 - \/ 3
$$x_{1} = 1 - \sqrt{3}$$
___ x2 = 1 + \/ 3
$$x_{2} = 1 + \sqrt{3}$$
x2 = 1 + sqrt(3)
The graph