Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x=4-3(3x-8)
-
Equation x/9+x=-10/3
-
Equation √(x^2-1)=2*x
-
Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
- 12*x-14*y=20
- Integral of d{x}:
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√(x^2-1)
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2*x
- Graphing y =:
- √(x^2-1)
- Derivative of:
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√(x^2-1)
-
2*x
- Limit of the function:
-
2*x
-
Identical expressions
- √(x^ two - one)= two *x
- √(x squared minus 1) equally 2 multiply by x
- √(x to the power of two minus one) equally two multiply by x
- √(x2-1)=2*x
- √x2-1=2*x
- √(x²-1)=2*x
- √(x to the power of 2-1)=2*x
- √(x^2-1)=2x
- √(x2-1)=2x
- √x2-1=2x
- √x^2-1=2x
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Similar expressions
- x^2+2x-3=0
- 8-5(2x-3)=13-6x
- √(x^2+1)=2*x
- 4^x-3*2^x+2=0
- 11+2x=55+3x
√(x^2-1)=2*x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{x^{2} - 1} = 2 x$$
$$\sqrt{x^{2} - 1} = 2 x$$
We raise the equation sides to 2-th degree
$$x^{2} - 1 = 4 x^{2}$$
$$x^{2} - 1 = 4 x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- 3 x^{2} - 1 = 0$$
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
$$a = -3$$
$$b = 0$$
$$c = -1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{\sqrt{3} i}{3}$$
Simplify
$$x_{2} = \frac{\sqrt{3} i}{3}$$
Simplify
$$\sqrt{x^{2} - 1} = 2 x$$
$$\sqrt{x^{2} - 1} = 2 x$$
We raise the equation sides to 2-th degree
$$x^{2} - 1 = 4 x^{2}$$
$$x^{2} - 1 = 4 x^{2}$$
Transfer the right side of the equation left part with negative sign
$$- 3 x^{2} - 1 = 0$$
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
$$a = -3$$
$$b = 0$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-3) * (-1) = -12
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{\sqrt{3} i}{3}$$
Simplify
$$x_{2} = \frac{\sqrt{3} i}{3}$$
Simplify
Sum and product of roots
[src]
sum
___
I*\/ 3
0 + -------
3
$$0 + \frac{\sqrt{3} i}{3}$$
=
___ I*\/ 3 ------- 3
$$\frac{\sqrt{3} i}{3}$$
product
___
I*\/ 3
1*-------
3
$$1 \frac{\sqrt{3} i}{3}$$
=
___ I*\/ 3 ------- 3
$$\frac{\sqrt{3} i}{3}$$
i*sqrt(3)/3
Numerical answer
[src]
x1 = 3.14703168507791e-35 + 0.577350269189626*i
x1 = 3.14703168507791e-35 + 0.577350269189626*i
The graph