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1. Given r2 - 82-1-10=19, to find the value of a.

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(d) The unknown quantity in each of the following examples, as won as in those given above, has always two values, as appears from the common rule ; but the negative, and imaginary foots being, in general, but seldom used in practical questions of this kind, are here suppressed.

5. Given; - ove-se, to find the value of a..

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- -6 1+z” 13. Given av(. -:) V& to find the value of a . Ans, w=(1+ ove)"

14. Given !, T-23–22, to find the value of a. Q: ! 1s 4 Ans. *=(; V5– ..)" 15. Given •v(-1)=v(*-*). to find the value

of c. Ans. x=444; V85* +a;

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The methods of expressing the conditions of questions 3f this kind, and the consequent reduction of them, till they are brought to a quadratic equation, involving only one unknown quantity and its square, are the same as those already given for simple equations. 1. To find two numbers such that their difference shall be 8, and their product 240. Let x equal the least number. Then will r-F8=the greater. And r(x+8)=z^+8x=240, by the question, Whence was —4+ v 16+240=–4+v/256, by the common rule, before given, Therefore r=16 – 4=12, the less number, And ac-1-8== 12+3=20, the greater.

2. It is required to divide the number 60 into two such parts, that their product shall be 864. Let a =the greater part, Then will 60 — r=the less, And r(60- a)=60x-a% =864, by the question, Or by changing the signs on both sides of the equation ac” – 60a;= -864,

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3. It is required to find two numbers such that their sum shall be 10(a), and the sum of their squares 58(b).

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4. Having sold a piece of cloth for 24l., I gained as much per cent. as it cost me; what was the price of the cloth 2

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5. A person bought a number of sheep for 80l., and if he had bought 4 more for the same money, he would have paid 11. less for each ; how many did he buy 7 Let a represent the number of sheep,

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6. It is required to find two numbers, such that their sum, product, and difference of their squares, shall be all equal to each other. Let x=the greater number, and y= the less.

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