Exponential Inequality Challenge: Simplify and Solve for x

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Homework Help Overview

The problem involves solving an exponential inequality of the form (5 + √24)x + (5 - √24)x > 98. Participants are exploring methods to simplify and approach the inequality.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to begin solving the inequality, mentioning attempts to apply logarithms without success. Some participants suggest hints related to the expression's structure, while others note specific values that satisfy the inequality.

Discussion Status

The discussion includes hints and insights shared among participants, with some indicating a specific value of x that satisfies the inequality. However, there is no explicit consensus on a complete method to solve the problem, and multiple interpretations of the approach are being explored.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the methods they can use or the information they can assume about the problem.

songoku
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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...
 
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hi songoku! :smile:

hint: 1/(5 - √24) =… ? :wink:
 


Notice that the LHS=98 if x=2.

ehild
 


tiny-tim said:
hi songoku! :smile:

hint: 1/(5 - √24) =… ? :wink:

hi tiny-tim :smile:

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 :smile:
 
songoku said:
hi tiny-tim :smile:

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"! :wink:
 

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