By Harley Flanders and Justin J. Price (Auth.)
Algebra and Trigonometry
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Additional info for Algebra and Trigonometry
We call r the «-th root of a and write r = ^/ä. The symbol >/~ is again called a radical. ) As with the square root, we shall write S/O = 0 because 0 n = 0. Examples: \/64 = 4 because 4 3 = 64, V^T = 3 because 3 4 = 81. Remark 1: If « is even, then ( —r)n = rw, so — v ^ is also an n-th root of a, a number whose w-th power is a. However, as with square roots, the symbol ~\/ä always means the unique positive n-th. root of a for a > 0. Remark 2: If n is odd, then negative numbers also have n-th roots.
1 / - ^ 28. ^±f/(iL±Z) 2 29. 4^I/4±J_ 30. (a + x + 4/x + 4 a3 + a a2 + \ Simplify: x + 2y\ xy / b)2/a2-b2 ab 46 1. BASIC ALGEBRA „ 35, (U2 V2\/U* V*\ t (xu — yv)2 + (xv + yu)2 x2 +y2 34. 36. x2y2 — 1 ** + * - 6 t2 + 4^ + A 12. C O M M O N ERRORS IN ALGEBRA The basic rules of algebra discussed in this chapter are indispensable in this course and all other mathematics courses you will take. It is worth the effort to master them now so you will avoid silly mistakes in the future. Let us Hst some of the most common types of errors in algebra.
Uv + 2w)2 15. ( x + / ) 3 16. (x - y)(X + y)(x* + y2) 17. (x + y + z)(2x - 7) 18. (y - z)(3x + 4y + z + 1) 19. (x + / - l)(x2 -y2 + x) 20. (x + y + z)(x + / - z) 21. (x2 + y2)(x2 - 3y2) 22. (x4 - y4)(x4 + y4) 23. (x + 7 + z)2 24. (ax + by + cz)(cx + Ζτμ + az) 25. (r + \)(s + 1)(/ + 1) 26. (r + *)(r - s)2 27. (a + Z>)(a + 2b)(a + 3Z>) 28. (a + &)(& + c)(c + a) 29. (x2 + 2xy - 2y2)(x2 - 2xy + 2y2) 30. (x + y + z)(x2 + 7 2 + z2 — xy — yz — zx). Is the expression a perfect square? If so, of what? 31.