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To find the sum of x squared and y squared, start by analyzing the conditions given. The first condition is x + y = 9, square both sides to get x squared + 2xy + y squared = 81. The second condition is x cubed + y cubed = 99, apply the sum of cubes formula to get x + y times x squared - xy + y squared = 99. Substitute x + y = 9 to get 9 times x squared - xy + y squared = 99. Divide both sides by 9 to get x squared - xy + y squared = 11. To eliminate xy, multiply both sides by 2 to get 2x squared - 2xy + 2y squared = 22. If we add equations 1 and 2, we get 3x squared + 3y squared = 103. Divide both sides by 3 to get x squared + y squared = 34.
