Final answer:
To find the critical values of x for the given probabilities, we need additional information about the distribution of x²₁₇ and x²₂₃.
Step-by-step explanation:
To find the value of x for which P(x²₁₇ ≥ x) = 0.10, we need to find the critical value of x²₁₇ at which the probability is equal to 0.10. Similarly, for P(x²₁₇ < x) = 0.10, P(x²₂₃ ≥ x) = 0.05, and P(x²₂₃ < x) = 0.05, we need to find the critical values of x²₂₃ at which the probabilities are equal to 0.10 and 0.05 respectively.
To find these values, we need additional information such as the distribution function or the probability density function for x²₁₇ and x²₂₃.