The expression you’ve provided seems a bit unclear, but it appears that you’re asking for the solution set of an equation involving x. Assuming you meant to write the equation as follows:
x³ + x – 5 = 0
This is a polynomial equation that we can solve for the variable x.
Solution:
This equation cannot be solved algebraically using simple factorization or roots, so we typically use numerical methods or graphing techniques to find solutions. However, from techniques such as the Rational Root Theorem, we can check for potential rational roots by substituting values for x. Trying out some values, we find:
- If x = 1:
1³ + 1 – 5 = 1 + 1 – 5 = -3 (not a solution) - If x = 2:
2³ + 2 – 5 = 8 + 2 – 5 = 5 (not a solution) - If x = -1:
(-1)³ + (-1) – 5 = -1 – 1 – 5 = -7 (not a solution) - If x = 0:
0³ + 0 – 5 = -5 (not a solution) - If x = 1.5:
(1.5)³ + 1.5 – 5 ≈ 3.375 + 1.5 – 5 = -0.125 (close to a solution) - If x = 1.6:
(1.6)³ + 1.6 – 5 ≈ 4.096 + 1.6 – 5 = 0.696 (not a solution) - If x = 1.7:
(1.7)³ + 1.7 – 5 ≈ 4.913 + 1.7 – 5 = 1.613 (not a solution)
Through these evaluations, we can see that a root lies between 1.5 and 1.6. More precise methods, like the Newton-Raphson method or numerical solvers, can help refine this value further.
In summary, the solution set is not easily expressible in a simple form, but it can be determined to be approximately x ≈ 1.5 using numerical methods. For exact values, one might resort to software or graphing calculators that can aid in finding the roots of polynomials.