Math Olympiad | How to solve for X in this problem ?

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[@ganale]

Superb n clever working

[@is7728]

∵It's indeed quadratic
∴It has 2 solutions, 1 and -1

[@MrTrashification]

Very nice. So many skills to key this

[@learncommunolizer]

Thank you very much!

[@knotwilg3596]

Set y =5^x then 5y+5/y=26 so 5y² - 26y +5 = 0
This is a quadratic equation with discriminant 676-100 = 576 = 24²
so y = (26+/- 24)/10 = 5 or 1/5 hence x = 1 or -1

[@Yureka-ox5jn]

Thanks ❤❤❤❤❤❤❤

[@cachotrelles4715]

👍👍👏👏👏👌 excelente

[@learncommunolizer]

Thank you very much!

[@brazo98]

Nice 🖖💪😻

[@learncommunolizer]

Thank you very much!

[@yuusufliibaan1380]

❤❤❤Very good thank you very much❤❤❤

[@learncommunolizer]

You're welcome 😊
Thank you very much!!!

[@miracbarsapaydn650]

X = 1

[@janisfrauenburgs3300]

25+1=26 so x=1 :)

[@user-dv8gv3hu4t]

Excellent

[@auxander]

1+25=26 so x=-1

[@l.w.paradis2108]

Yes, x = {1, --1}

[@l.w.paradis2108]

By simple inspection.

[@nil3010]

Oh no

[@SuperAnangs]

Only a blink I guess x=1

[@JPTaquari]

OK, cool little problem, but I don't see the point in doing the math, as the solution is visual:
The solution can only be 25 + 1 or 1 + 25
Ergo, X has to be +1 or - 1
That's All, Folks

[@knotwilg3596]

True. As you can see though, many respondents "see" 1 but don't see the symmetry that gives you -1.
Also, if the number on the right side were less convenient than 26, you need algebra.
Say the number is 126. Oh easy peasy 126 = 125 + 1, so 1+x = 3 and 1-x = 0 ... but that's impossible.

[@mudwangwu4779]

X=1

[@l.w.paradis2108]

Also, -- 1