rocdocmac 9 Posted April 20, 2019 Report Share Posted April 20, 2019 Find x in: Quote Link to post Share on other sites

1 Solution bonanova 85 Posted April 21, 2019 Solution Report Share Posted April 21, 2019 The solutions are Spoiler 1 and 2. Because Spoiler x ^{1/x} = (x^{2})^{1/x^2} = x^{ 2/x^2 } By inspection 1 and 2 are solutions, and a plot of the difference of x ^{1/x }and x^{ 2/x^x }shows sign changes (only) at 1 and 2. Also, for any value of x not equal to 0 (illegal division) or 1 (all powers of 1 are equal) dividing by x yields simply 1/x = 2/x^{2 }or more simply x^{2} = 2x. Cute. Quote Link to post Share on other sites

0 rocdocmac 9 Posted April 21, 2019 Author Report Share Posted April 21, 2019 Spoiler Indeed a very easy one! I was first thinking of having one find x and y in: "xth root of x = yth root of y" [or x^(1/x) = y^(1/y)] If x<>y, then only one solution: x = 2 and y = 4 Quote Link to post Share on other sites

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