2. Given 10x=x3+3 to find the values of x. Taking the positive sign, and cancelling, x2=3x. 3. Given 4x+3x=182 to find the values of x. 4. Given -7x=6 to find the values of x. Ans. x=3, or −1, or -2. 5. Given x3=37x+84 to find the values of x. Ans. x=7, or -3, or -4. 6. Given 2x+7x=474 to find the values of x. 7. Given 9x3-169x+280 to find the values of x. 8. Given x3-3x=322 to find the values of x. 1. There is a cubical block of marble; and if 50 be added to the number of square feet in half its surface, it will be equal to the number of cubic feet in its contents. contents of the block? What are the solid Then, 322 the superficial contents of one-half the surface of the block. Therefore, 3-3x2+50. Multiplying both sides by 8, 8x3-24x2+400. Adding and square of 4x, x+8x2+16x2=x1+40x2+400. 2. A gentleman having asked a lady her age, she replied, that if 29 times the square of her age were subtracted from twice its cube, the remainder would be 225. What was the lady's age? Adding 1 and the square of x, x+2x3+x2=x1+30x2+225. Evolution, x2+x=x2+15. x=15 years. 3. A boy, being asked what he gave for his books, replied, that if 51 times the square of the number of dollars he gave for them were subtracted from 6 times the cube of the number, the remainder would be 900. What was the price of the books? Ans. $10. 4. A man, being asked how many dollars he had in his pockets, replied, that if three times the cube of the number he had in one pocket were added to five times the square of the number he had in the other, he should have 272. Required the number he had in both pockets. Ans. $4. 5. A boat has been sailing two hours, with a light breeze, against a strong current; nineteen times the number of miles it has sailed is equal to the cube of that distance, added to thirty miles. How far has it sailed? Ans. It has gained either 3 miles or 2 miles, or it has lost 5 miles. MISCELLANEOUS QUESTIONS. 1. Multiply 7x+3√x3−√√x” by 0ÿ3. Ans. 7. Divide a3+x5 by a+x. Ans. aa—a3x+a2x2-ax3+x1. 8. Multiply y+x” by y—x. Ans. yTM+1+xTMy—xy”—x”+1. 11. Multiply 3x-a2 by 4√√√x2-a. Ans. 12-3ax-2a2x2+3a2x2+6a3x3+a*x*—a3x2—6a1x3 value of x. Ans. x=4. 15. Given (+28)(√/x+6)=(√x+38)(√x+4) to find the value of x. Ans. x=4. 16. Given (x-1)/2x-x2— to find x. √2±1 Ans. x= No2 17. Given x-2√x+2=1+√2-3x+2 to find x. 2m 18. Given a+x=2x2-5ax+b2 to find the value of x. 19. Given b=a+bx to find the value of x. of x. 20. Given (x-a)-(2x-36)=10a-+116 to find the value Ans. x=25a+246. 23. Given (a+22), (a-x2) to find the value of x. 24. Given =x+ Ans. x=4(a-1). (+)-(-6)** to find the value of x. х c 4a2c Ans. x=4b2+c *462+c2° 25. A gentleman travelled 252 miles. The first day he rode 4 miles, the last 128, and each day's journey was double the preceding one. How many days was he performing the journey? Ans. 6 days. 26. A gentleman dying left his sons an estate of $13,187.50. He bequeathed to his youngest son $1000, to the oldest $5062.50, |