mathematical puzzle ## One Equals Zero### Suppose \( x = 1 \).Then,\[ x^2 = x \]\[ \Rightarrow x^2 - 1 = x - 1 \]\[ \Rightarrow (x - 1)(x + 1) = x - 1 \]\[ \Rightarrow (x + 1) = 1 \]\[ \Rightarrow x = 0 \]So,\[ 1 = 0 \]Is this possible? What led to this ridiculous conclusion?---### Explanation:The logical steps taken here seem to conclude that \(1 = 0\), which is clearly a fallacy. The mistake in this derivation occurs at the step where \((x - 1)(x + 1) = x - 1\). Dividing both sides of the equation \((x - 1)(x + 1) = x - 1\) by \((x - 1)\) is erroneous because if \( x = 1 \), \( (x - 1) = 0 \), and division by zero is undefined. This leads to the false conclusion.### Illustration:The illustration beneath the text features a cartoon magician donning a top hat and performing sleight of hand. The magician is gesturing towards a table with the equation "1 = 0" whimsically displayed. The magician is also saying "TA DA!!", highlighting the absurdity and seemingly magical nature of the illogical mathematical conclusion. This visual underscores the deceptive nature of the false mathematical proof presented.### Reflection:Mathematical proofs require careful attention to the rules and properties of numbers, especially when it comes to operations like division. This example serves as a reminder to always ensure the validity of each step in a mathematical argument.

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Answered: 1. One Equals Zero Suppose x= 1. Then…

1. One Equals Zero Suppose x= 1. Then x² = X x² – 1 = x- 1 (x= 1)(x+ 1) = x = 1 (x+ 1) = 1 X = 0. So 1 = 0. Is this possible? What led to this ridiculous conclusion? 11 1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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