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.
A root difference inequality is an inequality that involves the difference of two or more square roots. It is typically used to compare the magnitude of two quantities.
To solve a root difference inequality, you must isolate the square roots on one side of the inequality and then square both sides to eliminate the square roots. The resulting inequality can then be solved using basic algebraic techniques.
Root difference inequalities follow the basic properties of inequalities, such as the addition, subtraction, multiplication, and division properties. However, when taking the square root of both sides, it is important to consider both the positive and negative roots.
Root difference inequalities can be applied in various fields, such as physics, economics, and engineering. For example, they can be used to solve problems involving distance, time, and velocity, or to compare the prices of two products.
Yes, there are some limitations to using root difference inequalities. They may not be applicable in situations where the quantities involved are complex or irrational numbers. Additionally, care must be taken when squaring both sides, as this may introduce extraneous solutions.