A Nice Algebra Problem | Math Olympiad | Exponential Equation

[@quynhnguyen3873]

EM CHÀO THẦY. CHÚC THẦY KHỎE

[@trojanleo123]

x = ln2/ln3

[@SALogics]

Yes, you are right! ❤

[@gaiatetuya92]

最初にxは実数とは書いていない。だから虚数解もある。

[@SALogics]

はい、あなたは正しいです！

[@quynhnguyen3873]

T =3^x. T^3 + T^2 + T -14 =0. F(2) =0. F(T): (T-2). ĐỂ ĐƯA VỀ A.B =0

[@adamnyback]

It's non-obvious how you came up with the idea to split -14 into -8, -4 and -2. How would you solve it if it was -15 or -13?

[@SALogics]

Because 8 = 2³ and 4 = 2²

[@adamnyback]

@SALogics Yes, but when I see a number like 14 my first thought is not that it can be split up like that. Similarly when I see the number 399 my first thought wouldn't be 7^3+7^2+7. Is there some method to do that easily or is it just trial and error?

[@SALogics]

@@adamnyback When we see m³ + m² + m then we think of spliting 14 = 2³ + 2² + 2

[@adamnyback]

@@SALogics How would you solve it if it was 15 or 399 instead of 14?

[@SALogics]

@@adamnyback 399 = 7³ + 7² + 7 and 15 = 3³ - 3² - 3