23. x x1y1 + y.

24. x3 — x2y\ + x3y‡ — xy + xły‡ – y§.

25. } √15, # √7, } $175.

26. 3 (2 — √3), § (3 √2 − 2√3), † ( √5 +. √ 3).

27. (2 + √2 - √6), ¿ (2 √3 + 3 √2 - √30), 5 + 2 √6.

28. a (x2 - x2y3
x2y3 + x3⁄4y* — xy + x3ys — y3),

's (3 - 32. 2 + 3. 23 – 3.2 + 3§. 2§ – 2§),

b

− xżył + y).

30. √6 + √2, √6 – √3, √√ 15 – √5.

6. Less than 5 when x lies between 2 and 3; greater than 5 for all values beyond these limits.

8. a satisfies the equation

4202 - (a + b 6 c)x + 2 (cab)

= 0.

2. From 0° to 90°, +; from 90° to 180°, — ; from 180° to 270°, +; from 270° to 360°, –

and 45°, 45° and 135°, 135° and 225°, 225° and 315° The corresponding signs of cos A

respectively.

sin A are +

+.

4. Cos 2 A is +, -, +, - respectively, as in Question 3.

1. 2, 3, 1, 1, 2, 1.5. 2. 5, 6, 1.5.

3. 10791812, 1.5563025, 1.6532125, 1.8750613,
2-6020600, 5740313, 1-8239087, 2-8696761.
4. 1-3172901, 3-3172901, 2.3172901, 3.3172901.
5. 1, 1, 3, 3.

6. 020912, 2091200, 20912, 20912.

7. I.3162760.

10. 3.1303338.

=

9. C 50 √6 (√3-1), b = 100 (√3 − 1).

4. A

=

5. A

=

=

45°, C = 75°.

9 (√6 ± √2).

105°, b = 6 (3/2/6), c = 12 (2-3).

75°, B = 60°, c = 26.

6. B 60° or 120°,

=

=

C 75° or 15°, c =

5 (3±√3).