test","extracted_subject":"MATH","extracted_chapter":"LOGARITHM, INDICES SURDS, PARTIAL FRACTION (OUT OF SYLLABUS)","extracted_topic":"INDICES AND SURDS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2043.png?top_left_x=532&top_left_y=712&width=532&height=270&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e73425d76b7ab31faf5","slug":"if-x-y-z-12-xsup2sup-ysup2sup-zsup2sup-96-frac1x-f","content":"If x + y + z = 12 & x² + y² + z² = 96 &\\(\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}\\)= 36\n\nthen value of x³ + y³ + z³ is","options":[{"_id":"68aa8a2c7f15af4716dadb43","text":"862","sequence":0,"isCorrect":false},{"_id":"68aa8a2c7f15af4716dadb44","text":"863","sequence":1,"isCorrect":false},{"_id":"68aa8a2c7f15af4716dadb45","text":"865","sequence":2,"isCorrect":false},{"_id":"68aa8a2c7f15af4716dadb46","text":"866","sequence":3,"isCorrect":true}],"correct_answer":"866","explanation":"(x + y + z)² = 144\n\n\\\\ åx² + 2åxy = 144\n\ñ åxy = 24\n\nNow\n\n\\(\\frac{\\sum xy}{xyz}\\)**=** 36\n\ñ xyz = \\(\\frac{2}{3}\\)\n\n\\\\ x³ + y³ + z³ – 3xyz = (x + y + z) (åx² – åxy)\n\n\\\\ åx³ – 2 = 12 (96 – 24)\n\ñ åx³ = 866","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:39.018Z","__v":0,"vector_store_id":"b1277862-2036-4856-9e65-accde09abadb","updated_at":"2024-08-30T21:49:39.018Z","isStarred":false},"params":{"questionSlug":"if-x-y-z-12-xsup2sup-ysup2sup-zsup2sup-96-frac1x-f"}}]}]]

Question: If x + y + z = 12 & x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 96 &\(\frac{1}{x} + \frac{1}{y} ...

Solution