Exponential Inequality Challenge: Simplify and Solve for x

songoku · Nov 8, 2012

Homework Statement

(5 + √24)^x + (5 - √24)^x > 98

inequalities
exponential

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 · Nov 8, 2012

hi songoku!

hint: 1/(5 - √24) =… ?

ehild · Nov 8, 2012

Notice that the LHS=98 if x=2.

ehild

songoku · Nov 8, 2012

tiny-tim said:

hi songoku!

hint: 1/(5 - √24) =… ?

hi tiny-tim

Wow what an insight !

ehild said:

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 · Nov 9, 2012

songoku said:

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"!