Solve for x 2^(x^3-x)=1

Problem

2(x3−x)=1

Solution

1. Identify the property of exponents that relates a base to the value 1. Any non-zero base raised to the power of 0 equals 1.

2=1

2. Equate the exponents by rewriting the right side of the equation with the same base as the left side.

2(x3−x)=2

3. Set the exponents equal to each other since the bases are identical.

x3−x=0

4. Factor the polynomial by taking out the greatest common factor, which is x

x*(x2−1)=0

5. Factor the difference of squares expression x2−1

x*(x−1)*(x+1)=0

6. Apply the zero product property to find all possible values for x by setting each factor to zero.

x=0

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x={−1,0,1}

Want more problems? Check here!