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Answers to Exercises; Chapter (^3 283) 1 1 1 n-l =- [ --- = x x+1 7x2 +^1 1 (x+ l)(nx+ 1)’ 6.6. We have t3+t2+15t-27 = A(t-3)+B+ ...
284 Answers to Exercises and Solutions to Problems Solutions to Problems Chapter 3 7.1. (a) (2x2 + 1)2 - 4x2 = (2x2 +2x + 1)(2x2 ...
Solutions to Problems; Chapter (^3 285) third zero is -(r + l/r). S ince -c/a is the product of the zeros and b/a is the sum of ...
286 Answers to Exercises and Solutions to Problems 7.10. Let u = r + s, v = rs. Then q(x) = x2 - ux + v and p(x) = (x - r)(x -s) ...
Solutions to Problems; Chapter (^3 287) b2 = 4(c+ 1). Th us, c+ 1 is a square, say u2, from which b = 2u. Conversely, ifb=2uandc ...
288 Answers to Exercises and Solutions to Problems and denominator (t + l)k. It suffices to show that the numerator is divisible ...
Solutions to Problems; Chapter 3 289 (Q - b)z] = (2~ - b)(02 - ab + b2). If a2 + b2 = ab (i.e. a/b is a primitive 6th root of un ...
290 Answers to Exercises and Solutions to Problems 8.5. First solution. Let U, v, w be the zeros of x3 + ax2 + 11x + 6 and u, v, ...
Solutions to Problems; Chapter 3 291 so that t > -15. Thus, -15 5 t 5 8. Checking possibiEties leads to the following polynom ...
(^292) Answers to Exercises and Solutions to Problems 8.12. Observe that 0 = -w7-x7-y7-%7=(x+y+%)7-x7-y7-%7 = 7(x + y)(y + %)(% ...
Solutions to Problems; Chapter (^3 293) (c) Cubing the three equations and adding (taking account of (a) and (b)) yields a3 + b3 ...
294 Answers to Exercises and Solutions to Problems Since 0 # 1, it is the second factor which vanishes and we obtain 1 = l-e+e2- ...
Solutions to Problems; Chapter 3 295 This is clearly nonnegative if 0 5 r + s < d. If d 5 r + s < 2d, then at least one of ...
296 Answers to Exercises and Solutions to Problems all unequal. However, let n = 2*m with m odd. Since the powers of 2 cannot be ...
Answers to Exercises; Chapter 4 8.30. We have the following table of solutions: Modulo the congruence is satisfied by n congruen ...
298 Answers to Exercises and Solutions to Problems then by Exercise 4.2, x : y : z = (br - cq) : (cp - ar) : (aq - bp). If there ...
Answers to Exercises; Chapter 4 299 2.4. Both equations lead to 0 = (x - 2)(4x - 7). (a) 2, 7/4; (b) no solutions. 2.5. (b) Let ...
300 Answers to Exercises and Solutions to Problems au2-u4+av -v2; d= bv+2uv2 - auv - u3v. Rearranging terms, we find that v2-(3u ...
Answers to Exercises; Chapter 4 301 [a(3v2w + w3d) + 2bvw + cw]J;i. Since 4 $ F, it f o 11 ows that both expressions in square ...
302 Answers to Exercises and Solutions to Problems and the points of intersection are (-1, -1) and (0, -1). 4.8. (a) The equival ...
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