Final answer:
To solve the equation x^4 - 9x^2 + 8 = 0 using u substitution, we substitute x^2 with the variable u and factor the quadratic equation to find the values of u. Substituting back x^2 for u gives us the solutions x = 1, x = -1, x = 2√2, and x = -2√2.
Step-by-step explanation:
To solve the equation x4 - 9x2 + 8 = 0 using u substitution, we can substitute x2 with the variable u. This gives us u2 - 9u + 8 = 0. Now, we can factor this quadratic equation as (u - 1)(u - 8) = 0. Setting each factor equal to zero, we get u - 1 = 0 and u - 8 = 0. Solving for u, we find u = 1 and u = 8.
Next, we substitute back x2 for u in each equation. For u = 1, we have x2 = 1, which gives us two possible solutions: x = 1 and x = -1. For u = 8, we have x2 = 8, which gives us two more solutions: x = 2√2 and x = -2√2.