Bonnycastle's Introduction to Algebra: Containing the Indeterminate and Diophantine Analysis, and the Application of Algebra to Geometry |
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Page 32
... factor which is common to them both , without in any respect changing the result . It may here also be farther added , that the common measure , or EXAMPLES . 1. Required the greatest common measure of the 32 ALGEBRAIC FRACTIONS .
... factor which is common to them both , without in any respect changing the result . It may here also be farther added , that the common measure , or EXAMPLES . 1. Required the greatest common measure of the 32 ALGEBRAIC FRACTIONS .
Page 33
... greatest common measure of the fraction -1 265 + 23 ° 2-1 ) x + x3 ( œ - OC x3 x or x2 + 1x - 1 ( x2 - 1 or tile x2 + x2 1 to h Whence +1 is the greatest common measure required . 2. Required the greatest common measure of the fraction ...
... greatest common measure of the fraction -1 265 + 23 ° 2-1 ) x + x3 ( œ - OC x3 x or x2 + 1x - 1 ( x2 - 1 or tile x2 + x2 1 to h Whence +1 is the greatest common measure required . 2. Required the greatest common measure of the fraction ...
Page 34
... common measure required . 4. It is required to find the greatest common measure of - - as Ans . x - α . 5. Required the greatest common measure of the fraction a4 a3 — a2x — ax2 + x3 ° - • Ans . a2x2 . 6. Required the greatest common ...
... common measure required . 4. It is required to find the greatest common measure of - - as Ans . x - α . 5. Required the greatest common measure of the fraction a4 a3 — a2x — ax2 + x3 ° - • Ans . a2x2 . 6. Required the greatest common ...
Page 35
... greatest common measure of the fraction x4--3ax3 - 8a2x2 + 18a3x - 8a + x3 - ax2 . 8a3x + 6a3 ― Ans . x2 + 2ax - 2a2 . 10. Required the greatest common measure of the fraction 5a5 + 10a4b + 5a3b3 a3b + 2a3b2 + 2ab3 + ba ° Ans . a + b ...
... greatest common measure of the fraction x4--3ax3 - 8a2x2 + 18a3x - 8a + x3 - ax2 . 8a3x + 6a3 ― Ans . x2 + 2ax - 2a2 . 10. Required the greatest common measure of the fraction 5a5 + 10a4b + 5a3b3 a3b + 2a3b2 + 2ab3 + ba ° Ans . a + b ...
Page 36
... greatest common measure ; and x + b ) x3- bax x2 + 2bx + b2 - bx the fraction required . x + b And the same answer would have been found , if a3 had been made the divisor instead of x2 + 2bx + b2 . 4. It is required to reduce 204 ენ ...
... greatest common measure ; and x + b ) x3- bax x2 + 2bx + b2 - bx the fraction required . x + b And the same answer would have been found , if a3 had been made the divisor instead of x2 + 2bx + b2 . 4. It is required to reduce 204 ენ ...
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Bonnycastle's Introduction to Algebra: Containing the ..., Pages 1-283 J. Bonnycastle,J. Ryan,J. F. Jenkins No preview available - 2017 |
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a²x² added Algebra answer arise arithmetical arithmetical mean ax² ax³ binomial bx² coefficients consequently cube root cubic equation decimal denominator denoted divisor equal EXAMPLES FOR PRACTICE expression factors find a number find the square find the sum find the value find two numbers former formula fourth fraction gallons geometrical geometrical progression give given equation given number greater greatest common measure Hence infinite series last term less logarithms method multiplied negative nth root number of terms perpendicular PROBLEM proportion quadratic equation quadratic surd quotient rational remain Required the number Required the sum required to divide required to find resolved result rule shillings side square number square root substituted subtracted surd third unknown quantity value of x Whence whole numbers yards