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((1-2x)^1/2)*(1-4x*(1+2x)^1/2)=8x^2-1

((1-2x)^1/2)*(1-4x*(1+2x)^1/2)=8x^2-1 equation

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Numerical solution:

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The solution

You have entered [src]
  _________ /          _________\      2    
\/ 1 - 2*x *\1 - 4*x*\/ 1 + 2*x / = 8*x  - 1
$$\sqrt{- 2 x + 1} \cdot \left(- 4 x \sqrt{2 x + 1} + 1\right) = 8 x^{2} - 1$$
The graph
Rapid solution [src]
         ______________
        /          ___ 
      \/  10 - 2*\/ 5  
x_1 = -----------------
              8        
$$x_{1} = \frac{\sqrt{- 2 \sqrt{5} + 10}}{8}$$
Sum and product of roots [src]
sum
   ______________
  /          ___ 
\/  10 - 2*\/ 5  
-----------------
        8        
$$\left(\frac{\sqrt{- 2 \sqrt{5} + 10}}{8}\right)$$
=
   ______________
  /          ___ 
\/  10 - 2*\/ 5  
-----------------
        8        
$$\frac{\sqrt{- 2 \sqrt{5} + 10}}{8}$$
product
   ______________
  /          ___ 
\/  10 - 2*\/ 5  
-----------------
        8        
$$\left(\frac{\sqrt{- 2 \sqrt{5} + 10}}{8}\right)$$
=
   ______________
  /          ___ 
\/  10 - 2*\/ 5  
-----------------
        8        
$$\frac{\sqrt{- 2 \sqrt{5} + 10}}{8}$$
Numerical answer [src]
x1 = 0.293892626146237
x1 = 0.293892626146237
The graph
((1-2x)^1/2)*(1-4x*(1+2x)^1/2)=8x^2-1 equation