Please show work algebraically Find all four solutions of th

Please show work algebraically.

Find all four solutions of the equation^6 x^4 - 4x = 1.

Solution

One solution was found :

                         x -0.249038219

Step by step solution :

Step  1  :

Polynomial Roots Calculator :

1.1    Find roots (zeroes) of :       F(x) = x⁴-4x-1
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which  F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -1.

The factor(s) are:

of the Leading Coefficient :  1
of the Trailing Constant :  1