Exponential Inequality Challenge: Simplify and Solve for x

[songoku]

Homework Statement

(5 + √24)^x + (5 - √24)^x > 98

Homework Equations

inequalities
exponential

The Attempt at a Solution

I don't know how to start...trying to put log to both sides could not take me anywhere because the LHS can't be simplified...

 

[tiny-tim]

hi songoku!

hint: 1/(5 - √24) =… ?

 

[ehild]

Notice that the LHS=98 if x=2.

ehild

 

[songoku]

hi songoku!

hint: 1/(5 - √24) =… ?

hi tiny-tim

Wow what an insight !

Notice that the LHS=98 if x=2.

ehild

Yes, but I think I should do some working to get that x


Thanks to both of you for the help. The problem is solved

 

[tiny-tim]

hi tiny-tim

Wow what an insight !

easy …whenever i see 1/(a + √b) or 1/(a + ib), i immediately think of multiplying top-and-bottom by the "conjugate"!