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how to find the sum of x squared and Y squared lets analyze the given conditions from the first condition X Plus y equals 9. Square both sides so we get x squared plus two x y plus y squared equals 9 squared 81 denote as one from the second condition X cubed plus y q equals 99 we apply the sum of cubes formula so we get X Plus y times x squared minus X Y plus y squared equals 99. but we know X Plus y equals nine plugin so we get 9 times x squared minus X Y plus y squared equals 99. both sides divided by 9 so we get x squared minus X Y plus y squared equals eleven our goal is one for the sum of x squared and Y squared so we want to eliminate x times Y is 2xy is negative X Y so both PSI times two so we get 2x squared minus two x y plus two y squared equals 22. we denote as two now one plus two we get x squared plus 2x squared so 3 x squared 2 X Y plus negative X Y zero y squared plus two y squared so 3y squared the right side 81 plus 22 103. both sides divided by three so we get x squa