Elements of Algebra: Including Sturms' Theorem |
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Page 64
... equa- tion , it becomes that is , 4x4-3 = 2 × 4 + 5 , 13 13 . Hence , 4 is the true value of x ; for , being substituted for x in the given equation , that equation is verified . 2. For a second example , take the equation 5x 4x 7 8 13x ...
... equa- tion , it becomes that is , 4x4-3 = 2 × 4 + 5 , 13 13 . Hence , 4 is the true value of x ; for , being substituted for x in the given equation , that equation is verified . 2. For a second example , take the equation 5x 4x 7 8 13x ...
Page 67
... equa- tion ; and it only remains to point out the best manner of making the statement . This part cannot , like the second , be subjected to any well- defined rule . Sometimes the enunciation of the problem furnishes the equation ...
... equa- tion ; and it only remains to point out the best manner of making the statement . This part cannot , like the second , be subjected to any well- defined rule . Sometimes the enunciation of the problem furnishes the equation ...
Page 77
... equa- tion can be multiplied by the same number , without destroying the equality ; therefore , multiply both members of the first equa- tion by b , the co - efficient of y in the second , and we have the equation - which , added to the ...
... equa- tion can be multiplied by the same number , without destroying the equality ; therefore , multiply both members of the first equa- tion by b , the co - efficient of y in the second , and we have the equation - which , added to the ...
Page 78
... equa- tion , the value of that unknown quantity could be deduced . If , now , both members of the first equation be multiplied by b ' , the co - efficient of y in the second , and the two members of the second by b , the co - efficient ...
... equa- tion , the value of that unknown quantity could be deduced . If , now , both members of the first equation be multiplied by b ' , the co - efficient of y in the second , and the two members of the second by b , the co - efficient ...
Page 82
... equa- tion , and adding them together , we have 43x - 2y = 121 16x + 9y = 84 The question is then reduced to finding the values of x and y , which will satisfy these new equations . Now , if the first be multiplied by 9 , the second by ...
... equa- tion , and adding them together , we have 43x - 2y = 121 16x + 9y = 84 The question is then reduced to finding the values of x and y , which will satisfy these new equations . Now , if the first be multiplied by 9 , the second by ...
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Common terms and phrases
affected algebraic quantities arithmetical arithmetical means arithmetical progression binomial co-efficient common difference consequently contain contrary signs cube root decimal deduced denominator denote derived polynomials divide dividend division entire number enunciation equa equation involving example expression extract the square factors figure find the square find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple letter logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose take the equation third tion transformed transposing unity unknown quantity whence whole number ах
Popular passages
Page 32 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 277 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Page 181 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 182 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 92 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 348 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 110 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 204 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.