5.

3. (2x+1)(-21).

Sides, 3, 5, 7 inches. Volumes, 27, 125, 343 cub. in.

ac

7. (1) 26.

(2) x = − 1, 1, 2 ; y = 0, f, 1.

(3) x = 2, y = 0,2 = 2.

8. When m = 4r — 1, real and positive value; when m = 4r + 1, real and negative value; when m = 2r, no real value ( being any integer).

9. d (a - b)t ;

d

a

(1) when a = b, they are always d miles apart. (2) when d also, they are always together.

10. 7.870... sq. inches.

= 0

2. x − ax1 — a2x3 + a3; x2 - (√2 − 1)x + √4 + √√2 + 1.

-

12. 156025: 11664; 4094'9. 14. 1991226, 2'066766; - 8899.

Straight line through points of intersection.

=

9 cot

2

IO.

*3979400, 3521826, Ï·3467875, 9824394.

11. 1289, and 2 cub. in.; 166·67 and 10.703 sq. in.

4. 502953178...

4 √ = b2 - 3(a2 + 462)* {(a + 2 √ − 62)* + (a − 2 √√ - 62) $1.

5.

(2) x = 1 + √ 2, − 3, 1, (− 3 + √17);

√ — 2, 1, 2,

(3) x = 1, y = 4, z = 27.

3- √17) and vice versâ.

7. £50.

5. A circle on the line joining the points as diameter.

4ac = 0.

II. 36989700, 2184267, 544068.

13. 16205 in.

5. (1) a2 2, a3 — 3a, a1 — 4a2 + 2 ;.

(2) 4a2 2, 8a3 - 6a, 16a1 - 16a2 + 2; 7√3.

(2) x =

3, 3+ √3;y=

2, - 3 - √3; and vice versâ.

≈ = (3 + √409).

(3) x = 3, y = 7, 5, z = 5, 7; x = 12, y = (3±409),

2=

7. 41 and 4 miles an hour.

8. Gold 24 oz., price £4 10s. per oz. ; silver 12 oz., price 5s. 3d. per oz.

x2+(2m − 3)x− 6m; (x2 + a2) (x + a)2 (x − a).

10. √2(a + 1); *1556302, 2100296, 1*1810658.

II.

1949'7 sq. in., 1949'7 cub. in. 12. 379'7 sq. yds. (π

пп 7п

3' 5' 15

12. 79° 6' 23", 40° 53′ 37′′.

14. 18°26′ 5′′.8.

I.-ALG. MENS.

July 1884.

1. (1) 5xy(xy) (x2 - xy + y2).

I.

(2) (a+b+c) (a2 + b2 + c2 — bc acab). Condition is (p + q)3 + (p + q)2 - a = o.

I

3. 2x+3(x2+12)3 {(x + √−y2)& + (x—~—y2)$}; 2a- · 3 0 + = c.

3