21. Given

y+16=2+y, to find the value of y.

Squaring each side, y+16=4+4√y+y; then (by 7, and transposition,) 16—4=4√√y, or 12=4√/y, ... (dividing by 4) 3=√/y; hence (13), squaring each side, y=9.

22. Given 9 ×√/y+33=√/9y+2, to find the value of y.

squaring each side, 9y+28=9y+4√√9y+4; by (7) 28=4/9y+4; ̈ ̈

by transposition, 28-4-4/9y, or 24=4√/9y;

24

..√9y=6; squaring each side, 9y=36;

23. Given a+y=b—√/2ay+y3, to find the value

of y.

Here, by transposition, √2ay+y2—b—a— -y; squaring each side, 2ay+y2= b2—2ab+a2+Qay +y2-2by;

..(by 7, and transposition,) 2by=b2-2ab+a2;

Here (10), multiplying the equation by (y+1). (y+2), or which is the same thing, multiply the

numerator of the first part of the equation by the denominator of the second part, and the numerator of the second part by the denominator of the first part, omitting the denominators,

(√y+34).(√y+2)=(√y+46).(√/y+1),

or y+36√/y+68±y+47√y+46;

(by 7 and transposition,) 68-46=47√/y—36√/y ;

22

or 22=11√y; ..√y==2;

... (13), squaring each side, y=4.

Since 3y-9-(3y-3).(√√/3y+3), the equation

(√/3y—3).(√/3y+3) √/3y+9

becomes

·+1=:

-+5;

√3y+3

3

then, by cancelling the like quantities in the numerator and the denominator of the first part of this equation, √3y+2+5

√3y-3+1=

3

... (10) 3/3y-9+3=1/3y+9+15;

by transposition, 3√/3y—√√3y=9+15+9—3,
or 2/3y=30; .·'. √/3y=15;

225 3

squaring each sidé, 3y=225; hence y= =75.

26. Given 13y+y4y+12=7y, to find the value of y.

Here (13), squaring each side, 13y+y√/4y+12=49y;

by transposition, y√4y+12=36y; dividing by y, √√4y+12=36; squaring each side, 4y+ 12=1296; .'. 4y=1296—12=1284;

Here (10), √7+yx√7+y+√yx√/7+y=28,

or 7+y+√/7y+y2=28;

by transposition, √/7y+y2=21—y; squaring each side, 7y+y=441-42y+y2; by transposition, 7y+42y=441;

or 49y=441;.*. y=9.

28. Given a+b=2a+26

to find the value of y.

y

Here (13), raising each side to the fifth power,

.. (ax. 4.) dividing the equation by a+b,

EXAMPLES FOR PRACTICE.

1. Given 4x+2=22, to find the value of x.

2. Given 3x-2=16, to find the value of x.

Ans. 5.

Ans. x 6.

3. Given 2x-ab, to find the value of x.

4. Given 18x+13-59-5x, to find the value of x. Ans. x=2.

5. Given 4x-4+ 62-3x, to find the value of x.

X 3

Ans. x=9.

6. Given+7+8, to find the value of x.

7. Given 4x2-7x=8x-x2, to find the value of x.

Ans. x=3.

8. Given ax2-abx=acx, to find the value of x. Ans. x=b+c.

bx dx

23. Given ~+=+=―r=4+(a+b).x, to find

the value of x.

Ans. x=.

abc.(4+r) ́ac(a—ab-b2)+b.(ab+cd)*