<prompt> Etsa bopaki ho bontša hore x2 y2nan  <response>: Instruction in English: Construct a proof to demonstrate that x2 y2 . Response in English: To prove that x2 y2, we must start by assuming that x and y are both real numbers. Starting with the equation x2 y2, we can take the square root of both sides to get x y, which means that x is equal to either y or negative y. To verify that this is true, we can square both sides of x y and x -y individually. If x y, then x2 y2. If x -y, then squaring both sides gives us x2 -y2, which simplifies to x2y2. So, in both cases, the end result is x2 y2, proving that our initial statement is true.Hence, we have demonstrated that x2 y2. . Response in Sesotho: Ho paka hore x2 y2, re tlameha ho qala ka ho nka hore x le y ke linomoro tsa sebele. Ho qala ka equation x2 y2, re ka nka motso oa lisekoere oa mahlakore ka bobeli ho fumana x y, ho bolelang hore x o lekana le y kapa negative y. Ho netefatsa hore sena ke nete, re ka sekoere mahlakore ka bobeli a x y le x -y ka bonngoe. Haeba x y, joale x2 y2. Haeba x -y, ho fata mahlakore ka bobeli ho re fa x2 -y2, e nolofatsang ho x2y2. Kahoo, maemong ana ka bobeli, sephetho ke x2 y2, ho paka hore polelo ea rona ea pele ke nete. Kahoo, re bontšitse hore x2 y2. 