LESSONS IN ALGEBRA. 



m 



5. Find the value of ' + A* 



a-~ l> 3 a + (, 



6. Find the yaluo of -J^n + i-t 



a 6 J 



.1 the value of 



h 1 



(a c) . (b c) . (* + c) 



i he valuo of 



lo 1 + 2jby 1 *-x*. 

 :nplify tho following fraction : 

 l-3x-2x 



-8 



11. Find tho valuo of 



13. Divide 



14. Extract the square root of x* + - + 2 ( t ) - 1 



15. Extract tho square root of x - xy + 2x + iy* - y + 1. 



1C. Extract tho cube root of 8"*- + SO? + 54 b - + 27 ' . 

 b b a a* 



17. Find the cube root of 125a - SOOa'b + 240ab - 64b. 

 la Simplify V^x + ^v/lG-'-c - V51- . 

 19. Simplify V(<*b - Cab + 9b) 



20. Simplify Vo s - %/(a 6 - nf) x Vo -r J^* - **) 



21. Find the continued product of (a+b)-, (a-b)-, (a+b)*, and (a-b)-. 



22. Multiply x + 2y* + 3i* by x - 2y + 3**. 



23. Simplify * + V^') - V^). 



*+ V 



/(/ o - l"v !> ) 



21. Simplify the following fraction : V \ (r^-fm ) ft 

 25. Add together tho fractions 



(x-l) d 

 ' 



26. Find the greatest common measure, and then reduce to its lowest 



27. Reduce to its lowest terms the fractions 

 a* + qib + a {,8 + b 



a + 3a a b + 4a'6 ; ' + 



28. Prove that 



29. Prove that 



, _ a* + cflb -f ob + b* 

 a* - 3ab -f 4ab - 3ab + b*" 



= 1. 



'(a-b).(a-c) ' (b-a).(b-c) T (c-a).(c-b) 



30. Which is greater, n + 1, or n + n' ? and which is greater, 

 **-!, or(x-l)'. 



31. If 240m = (12p + 5) n, show that ~. = ps + qd, and take the case 

 when m = 2, and 11 = 3 ; p = 13, and q = 4. 



32. Multiply 2a + 3b J- 1 by 3a-2b -J 1. 



a + b/^1 o + 2ab v /^ : l -b 

 ~~ a> 4 b 



. = (a + bv/"^!) x (a-b^l). 

 '(j;! + 2x- 3 y + xiy s ) and ^(x - 2xy 



86. Reduce n, o*, a^, and a* to equivalent quantities having the same 

 index ; also x*, y*, and T . 



k -a*byx*-a*. 



33. Show that 



84. Prove that c 



35. Find tho sum and difference of 



37. Divide _ 



, and 



o + J (o - 



38. Multiply V(* + 2) + 1 by ^(x- + 2) - 1. 



39. Divide to* + lie - 9x* - 19^ + 4** by x* - ^ + 3**- 4. 



40. Prove that xf- 1- e 5 + x*- > + *'+ x-1 = (x*- 1) .(*--* + 1 

 (**+!). (* + !)'. (-!)>. 



41. Find a fraction which, taken * - lly times, ahall produce 



42. What fraction multipUed by |x will produce --? 



43. Find the product of ?-?* by Q, and show the result in one line. 



C a R* 



44. Find bjr UM Maomtal UMONM tlM tth por oC 1 - *-. 

 : ,re inj.roi/n th UU Una ia UM tli 



>lnomil x y. 

 40. Find the 4th root of oUr. and tb*6tk root o- 



47. Find UM th root of - 



whw* U w odd 



48. Find the omba root of * + / + -*- 4* + 441* - S4X 



raw - 2*' in the form of Uw 5U. toot, nd U~ ia UM Com el 



be }th power. 

 50. Prove that 



51. Find the value of (^ + Jbd)*. 



52. Find the two middle terms of (a - b)" by the binomial 



53. Find the 9th term of (2ab - ed)". 



54. Find the 4th term of (a - b). 



55. Given Jd </* = Jdx, to find z. 



56. Oiven 17z* - 21 = x* -f 23, to find *. 



o 



57. Find tho value of x in the following equation : r.j}-7-S. 



58. GiTen* A /2Vi 4 -7= ^2, to find *. 



59. Given ' </7x*- 4 = - 2, to find z. 



60. Given 2a* (a* + *)"*= * + Va*~+~x, to find r. 



61. Given V* 9 ^ : *Vx* + x *-Jx x, to find x. 



62. Given2^x + iy-13= Jx-\y + 9, and 9Vr + Jf - 10= i/* + fy 

 + 72, to find x and v- 



63. Given7V*-2^y=^y + 15, and4^r -^y= v^x + 7, to find sandy. 



64. Given Jx ^y = 3, and Jz + Jy = 14, to find x and y. 



65. Given (* + 4) . (y-2) = ry, and (x-3) . (y + 5) = ry, to find z and y. 



66. Given Jx~^2 + 5Vy+ 3= 23, and ] ^x-2-3 yy+~3 = - 31, to 

 find x and y. 



67. Given 2.E* + 3y* = d, and x : y : : 2a : c, to find x and y. 

 6a Given xy = 20, and x* + y 1 = 41, to find x and y. 



69. Given x + y = 25 - 5, and xy = 57'5, to find x and y. 



70. Given x y = 2, and x y = 98, to find x and y. 



71. Given z + y = 18, and x' + y' = 170, to find * and y. 



72. Given x + y - 34, and z 5 + y = 27064, to find x and y. 



73. Given x - y = 7, and fL _ JL = 321* to find x and y. 



y * 



74. Given G.r' - 17xy + 12y' = 23, and 2r 3y = 4, to find * and y. 

 (N.B. Divide the first equation by the second.) 



75. Given x + y = 7, and x* y' = 21, to find x and y. 



76. Given x + y - z = 17, 2* - 2y + * = 9, and 3x-4y-i=4, to find 

 z, y, and :. 



77. Given x + y + z = 117, x y s = 63, and x y + i = 105, to find 

 x, y, and x. 



78. Given lOx - iy + }z = 50, 4r + 2y - \t = 22J, and 3x - 3y - Si = 0, 

 to find x, y, and z. 



79. Given xy = 40, xz = 10, and ys = 16, to flnd x, y, and i. 



80. Given x'y= 144, **'= 225, and yj= 400, to find x, y, and i. 



31. Given 3x - 2y + \z + w = 3, x + |y + s - \ie = 4, 2x - 4y + \ 

 + 2w = 5, and ix + Jy + $: 3u> = 6, to find ic, x, y, and z. 



82. Given x + y-- + w = 0, 2t-3y i + 5 6w = 33, 3x-r7j 

 + 3 - 4o + 5io = 62, lx - Jy -4-i* - i - Jw = 4, and 4x - 4y - 4 -HO* 

 810 = 92, to find v, w, x, y, and s. 



S3. Given x + x + 2y*= 24, and 2x- y f * 1, to find x and y. 



84. Given x ^5 + x'= i 3 , to find x. 



85. Given 2r - 4*' 4- 3 = 99, to find x. 



86. Resolve 8 into two factors, whereof the sum of the 5th powers 

 may be 1056. 



87. Given x+ xy + y'= 52, nd x- xy = - 8. to find x and y. 



88. Given x(x + t) = 104, and 3(x - t)i = 45, to find x and *. 



89. Given x+ **= x - t, and - *= xt, to find x and y. 



90. Given x* - xy+ x*y - x^ = 405. and x+ xy m 45, to find x and y. 

 (N.B. Divide the former by the latter.) 



91. Given x + y = 10, and x + y* = 1552, to find x and y. 



92. Given x + y = 7, and x* 4- y* = 3157. to find x and y. 



93. Given x - y = 4, and x* y* = 2320, to find x and y. 



91. Given x - y = 2, and ^ = 124, to flnd x and y. 

 V 



95. Given a + y > 11. and *- + -^ - 779jJ, to find x and y. 



V * 



96. Given x-y = 2,aad*_?lA. * *** * * nd 



V * 



97. Given x + y = 5. and xy = 6. to flnd c* + y* without finding r and y. 



98. Given x-y= 11. and T.J - K. to flnd x-i without finding x anU . 



99. Given x* - 2* + * = 1.12, to find x by quadratic*. 



100. Gireu * - 2x* + x* 359400, to find x by quadratic*. 



