Algebra for Schools and CollegesLongmans, Green & Company, 1895 - 309 páginas |
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Página 29
... Substituting this value of x in equation ( 1 ) , we have the identity ( 5 ) 2 = 2 . By comparing the several results obtained in the solving of the given equation , we may deduce the following rules : 91. I. Any term may be transposed ...
... Substituting this value of x in equation ( 1 ) , we have the identity ( 5 ) 2 = 2 . By comparing the several results obtained in the solving of the given equation , we may deduce the following rules : 91. I. Any term may be transposed ...
Página 41
... in the form of x2 Substituting - - m and - x2 − ( m + n ) x + mn . - ax + b . n form and + n in 108 , we have Now if we put a for m + n , and b for mn , we have x2 ― ax + b . 111. Hence , a trinomial of the form of x2 FACTORS . 41.
... in the form of x2 Substituting - - m and - x2 − ( m + n ) x + mn . - ax + b . n form and + n in 108 , we have Now if we put a for m + n , and b for mn , we have x2 ― ax + b . 111. Hence , a trinomial of the form of x2 FACTORS . 41.
Página 43
... Substituting n for n in ( 108 ) , we have , - x2 + ( m − n ) x - mn . If m > n , the quantity mn is positive . Now if we put a for ( m — n ) and b for mn , we have , x2 + ax b . - Hence , a trinomial of the form of x2 + ax into two ...
... Substituting n for n in ( 108 ) , we have , - x2 + ( m − n ) x - mn . If m > n , the quantity mn is positive . Now if we put a for ( m — n ) and b for mn , we have , x2 + ax b . - Hence , a trinomial of the form of x2 + ax into two ...
Página 44
... Substituting -m for m in ( 108 ) , we have , x2 + ( - m + n ) x mn . - ax - - b . If m > n , the quantity ( m + n ) is negative , and the sign of the middle term will be negative . Now if we put - a for ( — m + n ) and b for mn , we ...
... Substituting -m for m in ( 108 ) , we have , x2 + ( - m + n ) x mn . - ax - - b . If m > n , the quantity ( m + n ) is negative , and the sign of the middle term will be negative . Now if we put - a for ( — m + n ) and b for mn , we ...
Página 46
William Freeland. By changing the sign of p and q , and substituting in XI . , XII . , XIII . , XIV . , we have the resulting trinomials : ax2 + bx + c , ax2 + bx - ax2 bx + c , ax2 - bx ― C , C. 120. Therefore we may write the general ...
William Freeland. By changing the sign of p and q , and substituting in XI . , XII . , XIII . , XIV . , we have the resulting trinomials : ax2 + bx + c , ax2 + bx - ax2 bx + c , ax2 - bx ― C , C. 120. Therefore we may write the general ...
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Algebra for Schools and Colleges (Classic Reprint) William Freeland Sin vista previa disponible - 2018 |
Términos y frases comunes
a²+2ab+b² a²b a²b² a²x a³b a³b² a³b³ ab+b² ab¹ ab² ab³ algebraic arithmetical ax² b²)² binomial factors Clearing of fractions coefficient common factor Complete divisor Completing the square continued fraction convergent cube root decimal divided divisor equal EXAMPLE EXERCISE exponent expression Extract the square Find the H. C. F. find the number form of x² formula given gives harmonical mean Hence integral last term least common Least Common Multiple letters logarithm mantissa minus mixed surd monomial Multiply numbers whose product numbers whose sum operation indicated parenthesis Perform the operation permutations polynomial positive integer quadratic equation quotient radical Reduce remainder result second terms Solve the following square root subtract Transpose and unite trinomial unknown quantities Va² x²y x²y² xy³
Pasajes populares
Página 20 - 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.
Página 21 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 217 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Página 271 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 220 - If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r
Página 214 - In any proportion, the product of the means equals the product of the extremes.
Página 284 - For the first place can be filled in n ways, the second in n - 1 ways, the third place in n - 2 ways, and the rth place in n - (r - 1) ways.
Página 258 - If the coefficient of any term be multiplied by the exponent of a in that term, and the result divided by the exponent of x in the term increased by 1, the quotient will be the coefficient of the next following term.
Página 82 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.