An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJ. Munroe, 1837 - 276 páginas |
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Página 112
... Find the mth root of am n . 2. Find the mth root of a - mn 3. Find the square root of 9 a4 b2 ƒ 3 Ans . an Ans . απ . 12 g− 8 * ̧ 3a2b f − 6 g — 4 n . 4. Find the 4th root of Ans . a8 b20 c4 16d12z16 a2 b5 c Ans . 4 d3 z4 ― 5. Find ...
... Find the mth root of am n . 2. Find the mth root of a - mn 3. Find the square root of 9 a4 b2 ƒ 3 Ans . an Ans . απ . 12 g− 8 * ̧ 3a2b f − 6 g — 4 n . 4. Find the 4th root of Ans . a8 b20 c4 16d12z16 a2 b5 c Ans . 4 d3 z4 ― 5. Find ...
Página 113
... Find the mth root of cr et Ans . m bm c e - m m 9. Find the 5th root of ― Ans . α . 10. Find the square root of a . 11. Find the 3d root of 12. Find the mth root of a . a . - a Ans . at Ans . — a3 Ans . am 126. Corollary . By taking out ...
... Find the mth root of cr et Ans . m bm c e - m m 9. Find the 5th root of ― Ans . α . 10. Find the square root of a . 11. Find the 3d root of 12. Find the mth root of a . a . - a Ans . at Ans . — a3 Ans . am 126. Corollary . By taking out ...
Página 142
... Find the 9th root of y27 +27 y25 + 324 y23 +2268 y21 +10206 y 19+ 30618 y 17 + 61236 y 15+ 78732 y 13 + 59049 y11 19683 y9 . Ans . y3 + 3y . 141. Corollary . When the preceding method is applied to the extraction of the square , root ...
... Find the 9th root of y27 +27 y25 + 324 y23 +2268 y21 +10206 y 19+ 30618 y 17 + 61236 y 15+ 78732 y 13 + 59049 y11 19683 y9 . Ans . y3 + 3y . 141. Corollary . When the preceding method is applied to the extraction of the square , root ...
Página 143
... the square root of a given polynomial . Arrange its terms according to the powers of some letter , extract the square root of the first term for the first term of the root . Double the part of the root thus found for a divisor ...
... the square root of a given polynomial . Arrange its terms according to the powers of some letter , extract the square root of the first term for the first term of the root . Double the part of the root thus found for a divisor ...
Página 144
... Find the square root of 25 a1 24 ab3 + 16 b4 -- 42 30 a3 b + 49 a2 b2 Ans . 5 a2 - 3 ab + 4b2 . 3. Find the square root of 4x6 + 12 x3 + 5 x4 2x3 + 7x2 2 x + 1 . - -- Ans . 2x3 3x2 - — x + 1 . 4. Find the square root of aa . 2 as x + 3 ...
... Find the square root of 25 a1 24 ab3 + 16 b4 -- 42 30 a3 b + 49 a2 b2 Ans . 5 a2 - 3 ab + 4b2 . 3. Find the square root of 4x6 + 12 x3 + 5 x4 2x3 + 7x2 2 x + 1 . - -- Ans . 2x3 3x2 - — x + 1 . 4. Find the square root of aa . 2 as x + 3 ...
Outras edições - Ver tudo
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1858 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
Palavras e frases frequentes
2d Rem 3d root 4th root 94 become zero approximate values arithmetical progression binomial theorem coefficient commensurable roots contains the highest continued fraction continued product Corollary courier deficient terms denote dividend equal roots equal to zero factor Find the 3d Find the 4th Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence highest power integer last term least common multiple letter logarithm monomials number of terms obtained places of decimals polynomial Problem proportion quantities in example quotient radical quantities ratio real root reduced remainder required equation required root Scholium second term Solution Solve the equation square root substitution subtracted tained term multiplied tity unity unknown quan unknown quantity whence wine
Passagens conhecidas
Página 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 47 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 149 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 54 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Página 203 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Página 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.