Mister Exam

Other calculators

√(x^2-1)=2*x

√(x^2-1)=2*x equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
   ________      
  /  2           
\/  x  - 1  = 2*x
x2−1=2x\sqrt{x^{2} - 1} = 2 x
Simplify
Detail solution
Given the equation
x2−1=2x\sqrt{x^{2} - 1} = 2 x
x2−1=2x\sqrt{x^{2} - 1} = 2 x
We raise the equation sides to 2-th degree
x2−1=4x2x^{2} - 1 = 4 x^{2}
x2−1=4x2x^{2} - 1 = 4 x^{2}
Transfer the right side of the equation left part with negative sign
−3x2−1=0- 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=−3a = -3
b=0b = 0
c=−1c = -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
x1=−3i3x_{1} = - \frac{\sqrt{3} i}{3}
Simplify
x2=3i3x_{2} = \frac{\sqrt{3} i}{3}
Simplify
The graph
02468-8-6-4-2-1010-5050
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
         ___
     I*\/ 3 
x1 = -------
        3
x1=3i3x_{1} = \frac{\sqrt{3} i}{3}
Simplify
Sum and product of roots [src] 
sum
        ___
    I*\/ 3 
0 + -------
       3
0+3i30 + \frac{\sqrt{3} i}{3} 
=
    ___
I*\/ 3 
-------
   3
3i3\frac{\sqrt{3} i}{3} 
product
      ___
  I*\/ 3 
1*-------
     3
13i31 \frac{\sqrt{3} i}{3} 
=
    ___
I*\/ 3 
-------
   3
3i3\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
√(x^2-1)=2*x equation
    © Mister Exam – Calculator