Part 39

(b) x^2 + 2xy - a^2 - 2ay.

(c) (a + b)^2 + (a + c)^2 - (c + d)^2 - (b + d)^2.

4. Find H. C. F. of x^4 - x^3 + 2x^2 + x + 3 and (x + 2)(x^3 - 1).

5. Solve x/(x - 2) + (x - 9)/(x - 7) = (x + 1)/(x - 1) + (x - 8)/(x - 6).

6. The sum of three numbers is 51; if the first number be divided by the second, the quotient is 2 and the remainder 5; if the second number be divided by the third, the quotient is 3 and the remainder 2. What are the numbers?

~SMITH COLLEGE~

ELEMENTARY ALGEBRA

1. Factor e^(2x) - 2 + e^(-2x), x^(12) - 8, x^2 - x - y^2 - y, 18a^2x^2 -24axy - 10y^2.

2. Solve [7 + 4x + 3[2x^2 + 5x + 7]^(1/2)]^(1/2) - 3 = 0.

3. The second term of a geometrical progression is 3[2^(1/2)], and the fifth term is 3/16. Find the first term and the ratio.

4. Solve the following equations and check your results by plotting:

{ x^2 + y^2 - xy = 7, { x + y = 4.

5. Solve

1/(x^3) + 1/(y^3) = 243/8, 1/x + 1/y = 9/2.

6. In an arithmetical progression d = -11, n = 13, s = 0. Find a and l.

7. Expand by the binomial theorem and simplify:

8. The diagonal of a rectangle is 13 ft. long. If each side were longer by 2 ft., the area would be increased by 38 sq. ft. Find the lengths of the sides.

~SMITH COLLEGE~

ELEMENTARY ALGEBRA

1. Find the H. C. F. of 8x^3 - 27, 32x^5 - 243, and 6x^3 - 9x^2 + 4x - 6.

2. Solve:

(a) (2x + 5)^(-5) + 31(2x + 5)^(-5/2) = 32.

(b) (x - 1)^(1/2) + (3x + 1)^(1/2) = 4.

3. A farmer sold a horse at $75 for which he had paid x dollars. He realized x per cent profit by his sale. Find x.

4. Find the 13th term and the sum of 13 terms of the arithmetical progression

(2^(1/2) - 1)/2, (2^(1/2))/2, (1)/[2(^(1/2) - 1)], ....

5. The difference between two numbers is 48. Their arithmetical mean exceeds their geometrical mean by 18. Find the numbers.

6. Expand by the binomial theorem and simplify