Dear Aditya, A Golden Pre RMO Problem in 2017 in India

TL;DR

The video explains how to find values of X that create a geometric progression using fractional parts, and explores different definitions of fractional parts for negative numbers.

Transcript

okay I'd yet this right here is for you we are going to find X so that the fractional part of X the flow of X and X they are in geometric progression before we start off we will need to have a convention on what the fractional part of X is when X is a negative number when X is the positive number there's no argument for example the fractional part ... Read More

Key Insights

• 🥳 There are different ways to define fractional parts for negative numbers, and the choice depends on the situation.
• #️⃣ Geometric progressions require two numbers that can be multiplied by a constant to generate subsequent numbers.

Questions & Answers

Q: What are the three different ways to interpret the fractional part of a negative number?

The first way is to define it as the distance between X and the floor of X. The second way is to ignore the negative and the integer part, while the third way is to ignore the integer part but keep the negative sign before the fraction.

Q: How can you determine if two numbers form a geometric progression?

You can compare the ratio of the middle number divided by the previous number to the ratio of the next number divided by the middle number. If these ratios are equal, the numbers form a geometric progression.

Q: What is the quadratic equation derived in the video?

The quadratic equation is K^2 - K - 1 = 0, where K represents the ratio of the floor of X divided by the fractional part of X.

Q: How do you find the solutions for the quadratic equation?

By applying the quadratic formula, the solutions for K are 1 plus or minus the square root of 5, all divided by 2.

Summary & Key Takeaways

• The video discusses the convention for defining fractional parts of negative numbers and presents three ways to interpret the fractional part of -1.2.

• The concept of a geometric progression is explained, where two numbers can be multiplied by a constant to form a sequence.

• The process of finding X values that create a geometric progression using fractional parts is demonstrated, resulting in two sets of solutions.