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Substitute x 2 into the LHS and then RHS. You get 0 in both cases. Step 3. Remove brackets in the RHS. The highest power term is D[  . It is possible to get the other two terms too. This factorisation (turning a quadratic into a product) proves extremely useful in many engineering and scientific applications. 3 ALGEBRA: Exponentiation, Roots and Logarithms of Real Number Instructions for self-study • Revise Summaries on ALGEBRA and ORDER OF OPERATIONS • Revise Lecture 1 and study Solutions to Exercises in Lecture 1 using the STUDY SKILLS Appendix • Revise Lecture 2 using the STUDY SKILLS Appendix • Study Lecture 3 using the STUDY SKILLS Appendix • Attempt the following exercises: Q1.

Are all irrational 10 10 10 numbers. Answer: Also, log10 (1) is not a real number. The main message: if the base is positive the logarithm of a negative number cannot be a real number. com 1. All laws and rules of addition, multiplication and taking to integer power are first introduced for whole numbers and can be verified 45 (not proved) by substitution of whole numbers. It is then postulated (declared) that they extend to wider and wider number sets. 2. These operations can be applied to real numbers to produce results that are real too.

Variables: Irrational, Real and Complex Numbers Extracting an n-th root is an operation inverse to raising to power n. It is the third inverse operation we encounter. com 43 Elementary Algebra and Calculus ALGEBRA: Exponentiation, Roots and Logarithms of Real Number Question: what other inverse operations have we covered so far? Answer: As with subtraction and division, application of this new inverse operation might cause a difficulty: 1. First of all, the answer might not be unique. Question: what is a square root of 4, 9, 16 …?

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A treatise on elementary algebra by by James Hamblin Smith

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