perplexus.info :: Just Math : Some Real Numbers Sum 14

Some Real Numbers Sum 14 (Posted on 2024-11-09)

Find all possible values of a real number x that satisfy this equation:

(7+4√3)^x³-7 + (7-4√3)^x³-7 = 14

No Solution Yet Submitted by K Sengupta

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re: Solution

| Comment 2 of 3 |

(In reply to Solution by Kenny M)

It seems logical that the exponent must be an integer, otherwise the sum of the two terms will be hopelessly irrational. Trying a few leads to the exponent being = +-1, leading to x=2, 6^(1/3)

Posted by Kenny M on 2024-11-12 07:34:58

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