Algebraic Methods for Solving Complicated Equations with Variable x

[larry91]

Hi everybody!

I have to solve the following equation using algebraic methods: a=? such as 2^x + a^x > 3^x + 4^x for any x from ℝ.

I solved it using analytical methods. Using The Rolle Theorem, but I don't want to solve it in that way! The solution for a is 6

 

[Ray Vickson]

Hi everybody!

I have to solve the following equation using algebraic methods: a=? such as 2^x + a^x > 3^x + 4^x for any x from ℝ.

I solved it using analytical methods. Using The Rolle Theorem, but I don't want to solve it in that way! The solution for a is 6

Be careful: as written, your inequality fails for the real value x = 0. Perhaps you meant "≥". (In Mathematics, we need to be precise!) Also, of course, a solution is _any_ a ≥ 6. Perhaps the question asked for the smallest such a?

Finally, why do you not want to use Rolle's theorem?

RGV

 

[larry91]

Be careful: as written, your inequality fails for the real value x = 0. Perhaps you meant "≥". (In Mathematics, we need to be precise!) Also, of course, a solution is _any_ a ≥ 6. Perhaps the question asked for the smallest such a?

Finally, why do you not want to use Rolle's theorem?

RGV

Yes! The smallest value for a! and there is ≥. Sorry!
Using Rolle's theorem is quite simple to solve it... I don't want to solve it 'cause I need a solution for it... I just want to find an approach through we can solve it using algebraic methods!