This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 edition. Excerpt: ...Given 3x + lQx=--8 to find the value of x. SOLUTION. 0 (1). Adding 1 to both members of (1), makes the last term of the fint member a square. Thus, Sx' + lOx+O--1 (2). Adding now x' to both members of (2), makes the first term of th- first member a square. Thus, By examining the first member, we see that it ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 edition. Excerpt: ...Given 3x + lQx=--8 to find the value of x. SOLUTION. 0 (1). Adding 1 to both members of (1), makes the last term of the fint member a square. Thus, Sx' + lOx+O--1 (2). Adding now x' to both members of (2), makes the first term of th- first member a square. Thus, By examining the first member, we see that it would be a perfect square if the middle term were I2x instead of 10. But we can mate it 12 by adding 2x to both members, which being done, not onlj renders the first member a perfect square, but also the second one. Thus, AFFECTED QUADRATICS INVOLVING TWO UNKNOWN QUANTITIES. (326.) In solving equations of this character the usual plans of elimination may be employed. The student should adopt that plan which seems to be best for the example under consideration. 327. QUESTIONS PRODUCING AFFECTED QUADRATICS. QU E8TIO N.-4 and sold 130 yards of calico (of which 40 yards were A's, and 90 ffs), for $42. Now, A sold for $1, of a yard more than IS did. How many yards did each sell for $1? QUESTION S. 1. A merchant sold a quantity of cloth for $39, and gained -a much per cent, as the cloth cost him. What was the price of the cloth? An. $30. 2. There are two numbers whose difference is 9, and their sum multiplied by the greater produces 266. What are the numbers? Ans. 14 and 5, or--9 and--18$. 3. It is required to find two numbers, the first of which may be to the second as the second is to 16; and the sum of the squares of the numbers may be equal to 225. Ans. 9 and 12. 4. Bought two sorts of linen for 6 crowns. An ell of the finer cost as many shillings as there were ells of the finer. Also, 28 ells of the coarser (which was the whole quantity) were at such a price that 8 ells cost as many shillings as 1 ell of the finer. How...
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