How Many Integers Meet the Condition {√n - √(23×24)}² < 1?

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SUMMARY

The discussion centers on determining how many integers satisfy the condition {√n - √(23×24)}² < 1. The approximate value of √(23×24) is calculated to be around 23, leading to the conclusion that integers n must fall within the range of 22 to 24. The systematic approach involves recognizing that the square root approximation allows for a simplified analysis of integer values.

PREREQUISITES
  • Understanding of square roots and their properties
  • Familiarity with inequalities and their solutions
  • Basic algebraic manipulation skills
  • Knowledge of integer properties
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  • Study the properties of square roots in inequalities
  • Learn systematic approaches to solving inequalities
  • Explore integer solutions to quadratic equations
  • Investigate approximation techniques in mathematical analysis
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Mathematics students, educators, and anyone interested in solving inequalities and understanding integer solutions in algebraic contexts.

pratikaman
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How many integers satisfy {√n-√(23×24)}^2<1


I was able to solved this by trial and error method , but i want to know systematic step-wise solution.
 
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pratikaman said:
How many integers satisfy {√n-√(23×24)}^2<1


I was able to solved this by trial and error method , but i want to know systematic step-wise solution.


Show us what you did; perhaps your method was as good as anything.
 
Notice that the square root of 23x24 is approximately the square root of 23 squared. Since asked about only integers, this approximation suffices
 

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