Part 40

7. Solve:

1/x + 1/y = 3/2, 1/(x^2) + 1/(y^2) = 5/4.

8. Solve the following equations and check the results by finding the intersections of the graphs of the two equations:

{ x^2 = 4y, { x + 2y = 4.

~VASSAR COLLEGE~

ELEMENTARY AND INTERMEDIATE ALGEBRA

Answer any six questions.

1. Find the product of

2. Resolve into linear factors:

(a) 4x^2 - 25;

(b) 6x^2 - x - 12;

(c) a^2b^2 + 1 - a^2 - b^2;

(d) y^3 + (x - 3)y^2 - (3x - 2)y + 2x.

3. Reduce to simplest form:

(a) z/(1/x - 1/y) + y/(1 - y/x) - x/(1 - x/y).

(b) [-(x^3)^(1/2)]^(1/3) x (4y^(-3))^(1/2).

4. (a) Divide x^(3/2) - x^(-3/2) by x^(1/2) - x^(-1/2).

(b) Find correct to one place of decimals the value of [5^(1/2) + 7^(1/2)]/[2 - 3^(1/2)].

5. (a) If a/b = c/d, show that (a^2 + c^2)/(b^2 + d^2) = ac/bd.

(b) Two numbers are in the ratio 3 : 4, and if 7 be subtracted from each the remainders are in the ratio 2 : 3. Find the numbers.

6. Solve the equations:

(a) (x + 1)/(2) - 3/x = x/3 - (5 - x)/(6).

(b) 11x^2 - 11-1/4 = 9x.

(c) { x^2 - 2y^2 = 71, { x + y = 20.

7. A field could be made into a square by diminishing the length by 10 feet and increasing the breadth by 5 feet, but its area would then be diminished by 210 square feet. Find the length and the breadth of the field.

~VASSAR COLLEGE~

ELEMENTARY AND INTERMEDIATE ALGEBRA

Answer six questions, including No. 5 and No. 7 or 8. Candidates in Intermediate Algebra will answer Nos. 5-9.