A Maths Problem for You

Here’s a simple little maths problem for you to look at, if you like that sort of thing.

For what value of x does the following equation hold true?

x^n + 2.x^n+1 = x^n+3

Where x^3 is x cubed.

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10 Responses to A Maths Problem for You

  1. x=-1. I did enjoy this little puzzle but I had to get out a pencil and paper probably because I have become so very old! If this is an incorrect answer I am even older than I first thought. Nice image of the Andromeda Galaxy group.

  2. Greg Parker says:

    Blimey!! Well done – I wasn’t expecting that – and it wasn’t the answer I had 🙂 Can you find another solution for x? It is MUCH more difficult to find (but maybe not for you).

  3. x=1+or – square root of 2 ? so 3 solutions to x in all.

  4. Greg Parker says:

    You’re coming out with things I was not expecting here 🙂 The number I used to get this equality was in fact Phi, the Golden Ratio.

  5. Hi Greg was concentrating on tea rather than the problem. Made a very silly mistake re the square root of 2 solutions please discard. I told you I was old. Have however realised a nice way of coming up with -1 and Phi. Reduce the general equation by taking n=0.
    Therefore either:
    x+1 =0 or x=-1
    x^2-x-1=0 which is the formula for the golden ratio if you substitute Phi for x or is solvable using the quadratic formula giving two solutions (1+or-square root of 5)/2 presumably when minus it is the inverse of Phi. Bearing in mind I used to be an architect funny I should miss the Golden Ratio as a solution.
    Thanks for keeping me entertained on a cold afternoon.
    Regards George

  6. Greg Parker says:

    Hi George – Well you seem to have done a proper job on that one, I’m very impressed.My maths is nowhere near as good as yours, I should have seen the x = -1 solution from the beginning. I too am old. Unfortunately this April, if I make it that far, I will hit 70. As someone who didn’t expect to get past 30 you can imagine the shock.
    Regards Greg

  7. Thank you Greg but I strongly doubt that my mathematical skills exceed yours but on the arts side I’m a real dab hand with the Crayola wax crayons It did occur to me however that in accordance with Mr Euler as e^i.pi=-1 then e^ipi is a solution of x for all n and that very simple equation then links the golden ratio to e, i and pi by being part of a defined set. It then occurred to me that there might be limits upon n (do these 3 ,(-1, phi ,1/phi,) values for x work for minus values of n etc). Maths is troubling because the more you think about a problem the more it gets away from you. Much like looking out into the Cosmos!
    Best regards George

  8. Greg Parker says:

    Yes – it is fatal to keep looking deeper into maths problems. I was looking at the Tower of Power I^I^I^I (tetration) and soon found myself in the World of fractals. Quite disturbing 🙂

  9. Had to look up the ‘Tower of Power’ I think this is definitely above my ‘math pay grade’ . The first time I heard this expression, Frank Zappa used it to describe a joint.
    Don’t worry about the ‘seventy barrier’ you will steam through if you can negotiate the complex plane for fun. I am in my seventy fifth year on this planet and I occasionally have to take a moment to remember why going up ladders is unwise. I have noticed that increasing age has slowed my thinking, rendered multitasking dangerous and brought the delights of ’ buffering’ to my on board memory. Otherwise all is well and there is still lots to find out!

  10. Greg Parker says:

    You give me (a little) hope for the future, but this past year (69) was the first year I felt over 60. Before 2023 I felt like I was around 50.

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