Advanced Algebra for Colleges and SchoolsAmerican Book Company, 1902 - 608 páginas |
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Página 81
... divisible by the difference of the numbers . 2 . x2- y2 x + y 23 - y3 x + y x1 - y1 x + y x - y3 = x - y . = x2- xy + y2 , Rem . , -2 y3 . = x3 — x2y + xy2 — y3 . - = x1 — x3y + x2y2 - xy + y , Rem . , -2y . x + y From the above we ...
... divisible by the difference of the numbers . 2 . x2- y2 x + y 23 - y3 x + y x1 - y1 x + y x - y3 = x - y . = x2- xy + y2 , Rem . , -2 y3 . = x3 — x2y + xy2 — y3 . - = x1 — x3y + x2y2 - xy + y , Rem . , -2y . x + y From the above we ...
Página 82
... divisible by the sum of the numbers only when the powers are odd . 111. Hence , when n is a positive integer . PRINCIPLES . -1 . " y " is always divisible by x — y . 2. " y " is divisible by x + y only when n is even . 3. x " y " is ...
... divisible by the sum of the numbers only when the powers are odd . 111. Hence , when n is a positive integer . PRINCIPLES . -1 . " y " is always divisible by x — y . 2. " y " is divisible by x + y only when n is even . 3. x " y " is ...
Página 83
... divisible by x numbers and n is any positive integer . - y when x and y represent any two PRINCIPLE 2 xn - yn xn + xn - ly x + y | xn− 1 − xn − 2y + xn − 3y2 . - 1st Rem . , - xn - ly — yn — xn − ly — xn − 2y2 2d Rem . , 3d Rem ...
... divisible by x numbers and n is any positive integer . - y when x and y represent any two PRINCIPLE 2 xn - yn xn + xn - ly x + y | xn− 1 − xn − 2y + xn − 3y2 . - 1st Rem . , - xn - ly — yn — xn − ly — xn − 2y2 2d Rem . , 3d Rem ...
Página 84
... divisible by a x ( Prin . 1 ) . a6 26 is divisible by a + x ( Prin . 2 ) . Since a6x6 = ( a2 ) 3 — ( x2 ) 3 , ab -- - 26 may be regarded as the difference of two odd powers , and is , therefore , divisible by a2x2 ( Prin . 1 ) ...
... divisible by a x ( Prin . 1 ) . a6 26 is divisible by a + x ( Prin . 2 ) . Since a6x6 = ( a2 ) 3 — ( x2 ) 3 , ab -- - 26 may be regarded as the difference of two odd powers , and is , therefore , divisible by a2x2 ( Prin . 1 ) ...
Página 103
... divisible by a - b ; also by a3 — b3 , since a® — b¤ = ( a3 ) 2 — ( b3 ) 2 . When the even powers are regarded as squares , as in the second solution , the process may be regarded as factoring the difference of two squares . Separate ...
... divisible by a - b ; also by a3 — b3 , since a® — b¤ = ( a3 ) 2 — ( b3 ) 2 . When the even powers are regarded as squares , as in the second solution , the process may be regarded as factoring the difference of two squares . Separate ...
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Términos y frases comunes
a²b² a²x² ab² absolutely convergent algebraic sum arithmetical means arithmetical progression ax² binomial called cents coefficients column Commutative Law complex numbers continued fraction convergent convergent series cube root denominator difference digits divided dividend divisible established as follows EXAMPLES exponent expression factor Find the sum Find the value finite formula function geometrical mean geometrical progression geometrical series given equation Hence highest common divisor imaginary numbers inequality integer last term limit logarithm multiplied negative number nth root number of terms numerically less obtained polynomial positive integer positive number positive root PRINCIPLE quadratic quotient ratio real number reduced remainder represent result second term SOLUTION square root Substituting subtracted surd third Transposing twice units unknown number variable x²y x²y²
Pasajes populares
Página 212 - ... and if the number is divided by the sum of its digits, the quotient is 21 and the remainder 4.
Página 134 - Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction.
Página 343 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Página 41 - A term may be transposed from one member of an equation to the other, provided its sign is changed.
Página 435 - The number of permutations of n different things taken r at a time is denoted by „Pr.
Página 424 - The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the dividend.
Página 40 - The process of changing a term from one member of an equation to the other is called Transposition.
Página 331 - PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the difference between the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Division.
Página 323 - A farmer has two cubical granaries. The side of one is 3 yards longer than the side of the other, and the difference in their solid contents is 117 cubic yards.
Página 426 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.