Page:Elementary algebra (1896).djvu/354

336 ALGEBRA. 19. Simplify -  {2 - 6} 20. Find the sides of a rectangle the area of which is unaltered if its length be increased by 2 feet while its breadth is diminished by 1 foot, and which loses f of its area if its length be diminished by 2 feet and its breadth by 4 feet. 21. The first term of a G. P. exceeds the second term by 1, and the sum to infinity is 81 : find the series. 22. Find the number of permutations which can be made from all the letters of the word 3Iississip2n. 23. Solve (i.) x + 2 + 4x + 1 - 9x + 7 = 0. (ii.) 2x-3 x - 2 + 1 = 2 x-2 - 1. (iii.) 2 x-6+x + 3 x-2 = 4 x + 3 (iv.) 3 x - a - 3 x — b = 3 b — a. 24. Find the condition that one root of ax^2 + bx + c = 0 shall be n times the other. 25. Find the value of x^3 — 3x^2 — 8x + 15 when x = 3 + i. 26. Given log 648 = 2.81157, log 864 = 2.93651, find the logarithm of 3 and of 5. 27. Two trains run, without stopping, over the same 36 miles of rail. One of them travels 15 miles an hour faster than the other and accomplishes the distance in 12 minutes less. Find the speeds of the two trains. 28. Extract the square root of 9x^4 - 2x^3y + 163 9 x^2y^2 - 2 xy^3 + 9y^4. 29. Find, by logarithms, the value of {{15(.318)^1 7} 16} {1 11} 30. Simplify {1+ax^-1 a^-1x^-1} \times {a^-1 - x^-1} {a^-1x - ax^-1} ÷ {ax^-1} {x-a}. 31. The men in a regiment can be arranged in a column twice as deep as its breadth; if the number be diminished by 206, the men can be arranged in a hollow square three deep having the same number of