Key to professor Young's Algebra

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J. Souter, 1835 - 196 páginas
 

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Página 87 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 165 - Find such a value of x as will render rational the expression 6x — 2. CASE 6. When the proposed expression can be divided into two parts, one of which is a square, and the other the product of two factors.
Página 4 - When the dividend is a compound quantity, and the divisor a simple one, then each term of the dividend must be divided separately, and the resulting quantities will be the quotient required.
Página 112 - PROBLEM I. To reduce a rational quantity to the form of a surd. RULE. Raise the quantity to a power...
Página 164 - If we take p = 3, we shall have x = 9|, .-. the two numbers are :1! , and 6$. 2. Find two numbers, whose difference shall be equal to a given number a, and the sum of whose squares shall be a square. CASE 4. When a is a square, or when the expression is of the form v/aV + 6x + c. Put ^oV 4- bx + с = ax + p, or а*x' + 6x + с = a3x* + 2pax + p3, c „3 then bx + с = 2pax + p', .-. x = f—r.
Página 3 - When the multiplicand is a compound quantity, and the multiplier a simple quantity.
Página 177 - ... Quadratic Equations will be learnt by the examples which we shall give in this chapter, but before we proceed to them, it is desirable that the student should be satisfied as to the way in which an expression of the form is made a perfect square. Our rule, as given in the preceding Article is this : add the square of half the coefficient of the second term, that is, the square 2 of ^ , that is, -т- . We have to shew then that a' x + ax + -r4 is a perfect square, whatever a may be.
Página 164 - ... being any number whatever. 3. Find a number such, that if its square be multiplied by 7, and the number itself by 8, the sum of the products shall be a square. 4. Find a number such, that if its square be divided by 10, and the number itself by 3, the difference of the quotients shall be a square.
Página 170 - To find such values of x as will render rational the expression •S/<MM + bx3 + ex2 + dx + e.
Página 133 - Problem I. — To find the first term of any order of differences. Let the series be a, b, c, d, e ......... ; then, the respective orders of differences are, 1st order, I — a , c — I , d — c , e — d, .... 2d order, c— 26+« , d— 2c+6 , e— 2d+c ...... 3d order, d— 3c-f-3Z>— a, e— 3c£+3c— 6, ...... 4th order, e — 4d-j-6c — 46-|-o.

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