11 3 50. Required the square root of xa—3x3+ 4 4 +16 1 3 Result, x x+ 1 1 51. What is the 3d root of æo—_—_—æ3+ 52. Required the square root of a2+2b. 3 2 48 54 SECTION IV. EQUATIONS. 41. An equation is an algebraic expression, indicating that one quantity, or combination of quantities, is equal to another. The quantity, or combination, which stands on either side of the sign of equality, is called a member of the equation. Thus, ax+bx=ab+cd, is an equation, of which axs +bx is the first member, and ab+cd the second. 42. In the application of algebra to the solution of problems, the quantities concerned, both those which are given, and those which are required, are usually represented by symbols, and the conditions of the problem translated into the language of algebra. One or more equations are thus formed, including unknown as well as known quantities. 43. The number of independent equations required for the solution of a problem, is equal to the number of unknown quantities employed. 44. A simple equation is one which includes only the first or single power of the unknown quantity or quan- . tities, as ax+b=cx-d. 45: A quadratic equation, is one which includes the square of the unknown quantity. An equation which contains no power of the unknown quantity but the square, is called a simple quadratic, as ax=b; but, when the square and simple power of the unknown quantity are both included, it is called an adfected quadratic equation; as x2-ax-bc. 46. A cubic equation, is one which contains the cube of the unknown quantity; as x3+ax®+bx=c. 47. A biquadratic equation, is one which contains the fourth power of the unknown quantity; as x*+a*x2+c3x =b3d3. 48. Equations, in general, are said to be of as many dimensions as there are units in the index of the highest power of the unknown quantity. 49. In general, an equation which contains but one power of the unknown quantity is called a pure equation; thus, x=b+c, is called a pure quadratic equation; x3=b, a pure cubic equation, &c. |