Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=-100
-
Equation 9+10(3x-10)=2
-
Equation -7*x=4
-
Equation 10x-2(4x-5)=2x+10
- Express {x} in terms of y where:
- 4*x-4*y=-19
- -16*x+18*y=9
- 4*x-1*y=12
- 7*x-19*y=-8
- Graphing y =:
- sqrt(3-2*x^2)
-
Identical expressions
- sqrt(three - two *x^ two)= one
- square root of (3 minus 2 multiply by x squared ) equally 1
- square root of (three minus two multiply by x to the power of two) equally one
- √(3-2*x^2)=1
- sqrt(3-2*x2)=1
- sqrt3-2*x2=1
- sqrt(3-2*x²)=1
- sqrt(3-2*x to the power of 2)=1
- sqrt(3-2x^2)=1
- sqrt(3-2x2)=1
- sqrt3-2x2=1
- sqrt3-2x^2=1
-
Similar expressions
- sqrt(3+2*x^2)=1
sqrt(3-2*x^2)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{3 - 2 x^{2}} = 1$$
$$\sqrt{3 - 2 x^{2}} = 1$$
We raise the equation sides to 2-th degree
$$3 - 2 x^{2} = 1$$
$$3 - 2 x^{2} = 1$$
Transfer the right side of the equation left part with negative sign
$$2 - 2 x^{2} = 0$$
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
$$a = -2$$
$$b = 0$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = 1$$
Because
$$\sqrt{3 - 2 x^{2}} = 1$$
and
$$\sqrt{3 - 2 x^{2}} \geq 0$$
then
$$1 \geq 0$$
The final answer:
$$x_{1} = -1$$
$$x_{2} = 1$$
$$\sqrt{3 - 2 x^{2}} = 1$$
$$\sqrt{3 - 2 x^{2}} = 1$$
We raise the equation sides to 2-th degree
$$3 - 2 x^{2} = 1$$
$$3 - 2 x^{2} = 1$$
Transfer the right side of the equation left part with negative sign
$$2 - 2 x^{2} = 0$$
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
$$a = -2$$
$$b = 0$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-2) * (2) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = 1$$
Because
$$\sqrt{3 - 2 x^{2}} = 1$$
and
$$\sqrt{3 - 2 x^{2}} \geq 0$$
then
$$1 \geq 0$$
The final answer:
$$x_{1} = -1$$
$$x_{2} = 1$$
Numerical answer
[src]
x1 = 1.0
x2 = 1.00000000000001 - 2.29357658304174e-14*i
x3 = 1.0 - 7.34230992648723e-16*i
x4 = -1.0
x5 = -1.0 + 7.37283988973141e-18*i
x6 = -1.00000000000015 + 3.17331468384823e-13*i
x7 = 1.00000000000024 - 5.11807934893169e-13*i
x8 = 1.0 - 1.18366876199835e-19*i
x9 = 1.0 - 1.47194975295652e-17*i
x10 = -1.0 + 1.35175819520003e-14*i
x11 = -1.0 + 4.06521773899487e-16*i
x11 = -1.0 + 4.06521773899487e-16*i