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Curated by: Khan Academy India - English (11 videos)
Given a clue about two numbers and their GM, prove that their ratio is a given irrational number. Another hairy problem. Although this problem is typically categorised as a GM problem, the only place where we need the GM formula is the first step. After that, we leverage a number of prerequisites from linear equations, quadratic equations, rationalisation, etc. This is what truly makes this problem challenging. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! (https://www.khanacademy.org/math/ncert-class-11/xea4762213f311c5e:sequences-and-series-ncert-new/xea4762213f311c5e:geometric-progression/e/geometric-series) Timestamps: 00:00 Problem (Prove that the ratio of terms is a given constant) 00:41 Solution (Leveraging the formula for GM) 01:53 Introducing x as the ratio of terms 02:42 Solving the quadratic to find x 03:51 Making sense of the solution (larger value) 05:13 Making complete sense of the solution (smaller value) Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Ashish Gupta