114. If a=1, b=2, c=3, d=4, find the value of ab+be+ca 1 +3(aa +bb + cc) (++증). 115. I rode one-third of a journey at 10 miles an hour, one-third more at 9, and the rest at 8 miles an hour; if I had ridden half the journey at 10, and the other half at 8 miles per hour, I should have been half a minute longer on the way: what distance did I ride? 116. The product of two factors is (3x+2y)3— (2x+3y)3, and one of the factors is x-y; find the other factor. 117. If a+b=1, prove that (a2 — b2)2=a3 + b3 — ab. (2) m3 — n3 — m (m2 — n2) + n (m − n)2. (2) x2-6xy+11y2=9) x-3y=1) (a − b)1 − 2 (a2 + b2) (a − b)2+2 (aa + b1). 122. Find the H.C.F. of a2b+b2c-abc - ab2 and ax2+ab-a2-bx2. 123. A village had two-thirds of its voters Republicans: in an election 25 refused to vote, and 60 went over to the Democrats; the voters were now equal. How many voters were there altogether? x2+(a−1) x3- (2a+1) x2 + (a2+4a−5)x+3a+6 127. Resolve into factors: (1) x2+5xy-24y2+x-3y. (2) 23_1. 128. Find the square root of p2 - 3q to three terms. x-5 X- 6 X- 1 x-2 = 129. Solve (1) (2) ax+1=by+1=ay+bx. 130. Find the H. C. F. of 3x2+(4a−2b) x − 2ab+a2 and 131. Simplify - - 132. At a cricket match the contractor provided dinner for 27 133. Prove that x(y+2)+~+ У is equal to a, if x3+2ax2+a2x+2a3 and x3-2ax2+a2x-2a3. 137. Resolve 4a2 (x3+18ab2) –− (32a5+9b31⁄23) into four factors. - 140. Multiply x2+2y+322 by x2 - 2y2 - 322. 141. Walking 44 miles an hour, I start 1 hours after a friend whose pace is 3 miles an hour: how long shall I be in overtaking him? 142. Express in the simplest form 149. Find the square root of (a-1)*+2(a1+ 1) − 2 (a2+1) (a− 1)2. 150. How much are pears a gross when 12 more for a dollar lowers the price five cents a dozen? 151. Show that if a number of two digits is six times the sum of its digits, the number formed by interchanging the digits is five times their sum. 152. Find the value of 1 1 1 (a−b) (b−c) ̄ (b−c)(a−c) — (e−a) (b− a)· 153. Multiply 157. Find the H. C. F. of (p2-1) x2 + (3p − 1) x-p(p-1) and p(p+1) x2 - (p2 - 2p − 1) x − (p −1). 158. Reduce to its simplest form 160. A clock gains 4 minutes a day. What time should it indicate at 6 o'clock in the morning, in order that it may be right at 7.15 P.M. on the same day? 161. If x=2+√2, find the value of x2+ 4 x2. + + (b− a) (c− a) 1 (c—b)(a−b) † (a−c) (b − c) 164. Find the product of √5, 72, 780, 75, and divido 165. Resolve 9x3y2 — 576y2 – 4x3+256x2 into six factors. 168. Find the H. C. F. and L.C. M. of 20x1+x2-1, 25xa +5x3 − x − 1, 25x1 – 10x2 + 1. 169. Solve (1) a+x+√2ax+x2=b. 170. The price of photographs is raised $3 per dozen, and customers consequently receive ten less than before for $5: what were the prices charged? |