Find the number of triples of real numbers (a, b, c) such that a 20 + b 20 + c 20 = a 24 + b 24 + c

Question

Find the number of triples of real numbers (a, b, c) such that a 20 + b 20 + c 20 = a 24 + b 24 + c 24 = 1 .

Accepted Answer

{"content":[{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 1:","type":"text"},{"text":" a20 + b20 + c20 = a24 + b24 + c24 = 1","type":"text"}]},{"type":"paragraph","content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 2:"},{"text":" If both equation have to satisfy","type":"text"}]},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 3:"},{"text":" =>     Either ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" or ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"text":" or ","type":"text"},{"attrs":{"latex":"c"},"type":"math_inline"},{"text":" = ±1","type":"text"}],"type":"paragraph"},{"type":"paragraph","content":[{"marks":[{"type":"bold"}],"text":"Step 4:","type":"text"},{"type":"text","text":" And other have to be 0."}]},{"content":[{"marks":[{"type":"bold"}],"text":"Step 5:","type":"text"},{"text":" So, if ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" = 1","type":"text"}],"type":"paragraph"},{"content":[{"text":"Step 6:","type":"text","marks":[{"type":"bold"}]},{"text":" =>     b=c=0","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 7:","type":"text"},{"text":" If ","type":"text"},{"attrs":{"latex":"a"},"type":"math_inline"},{"text":" = –1","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 8:","type":"text"},{"type":"text","text":" =>     b=c=0"}],"type":"paragraph"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 9:"},{"text":" Similarly, for ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"type":"text","text":" and "},{"attrs":{"latex":"c"},"type":"math_inline"},{"text":" if ","type":"text"},{"attrs":{"latex":"b"},"type":"math_inline"},{"type":"text","text":" = ±1"}],"type":"paragraph"},{"content":[{"text":"Step 10:","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" =>     a=c=0"}],"type":"paragraph"},{"content":[{"text":"Step 11:","type":"text","marks":[{"type":"bold"}]},{"text":" And if ","type":"text"},{"attrs":{"latex":"c"},"type":"math_inline"},{"text":" = ±1","type":"text"}],"type":"paragraph"},{"content":[{"type":"text","marks":[{"type":"bold"}],"text":"Step 12:"},{"text":" =>     a=b=0","type":"text"}],"type":"paragraph"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 13:","type":"text"},{"text":" Total triples = 6.","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution