An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 104
... equation with one unknown quantity from the two equations 23+ y3 = a , 25y5 = b , by the elimination of x . Ans . ( y3 — a ) 5 — ( ÿ5 — b ) 3 — 0 . 3. Obtain one equation with one unknown quantity from the two equations x2 + y2 = 2 , x2 ...
... equation with one unknown quantity from the two equations 23+ y3 = a , 25y5 = b , by the elimination of x . Ans . ( y3 — a ) 5 — ( ÿ5 — b ) 3 — 0 . 3. Obtain one equation with one unknown quantity from the two equations x2 + y2 = 2 , x2 ...
Page 106
... Solve the two equations y x3 - 23 + x = = 3 , y x ( y x2 + 1 ) — x3 + x = 6 . - Solution . The elimination of x gives 3y - 3 : = 0 , or y 1 ; which , being substituted in the first of the given equations , produces X 3 . 11. Solve the two ...
... Solve the two equations y x3 - 23 + x = = 3 , y x ( y x2 + 1 ) — x3 + x = 6 . - Solution . The elimination of x gives 3y - 3 : = 0 , or y 1 ; which , being substituted in the first of the given equations , produces X 3 . 11. Solve the two ...
Page 136
... 23. Multiply a3 + b2 by ↓ a3 — √ b2 . m m 24. Divide a by √ b . Ans . aa - b4 . ma Ans . b 25. Divide a by a ... Equation from Radical Quantities . 204. Problem 136 [ CH . V. § II . ALGEBRA .
... 23. Multiply a3 + b2 by ↓ a3 — √ b2 . m m 24. Divide a by √ b . Ans . aa - b4 . ma Ans . b 25. Divide a by a ... Equation from Radical Quantities . 204. Problem 136 [ CH . V. § II . ALGEBRA .
Page 174
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of Quadratic Equations higher than the Second Degree . from which we obtain , by art . 224 , { B ± √ ( ~ AM + Į B2 x = A. 2. Solve the equation ... 23 = 56 .
To which are Added Exponential Equations and Logarithms Benjamin Peirce. Examples of Quadratic Equations higher than the Second Degree . from which we obtain , by art . 224 , { B ± √ ( ~ AM + Į B2 x = A. 2. Solve the equation ... 23 = 56 .
Page 175
... Solve the equation ( x2 + 5 ) 2 — 4 x2 = 160 . Ans . x 3 , or √ — 15 . 11. What two numbers are they , whose product is ... 23 y ) 3 + ( x2 — 23 y ) 2 + ( x2 — 23 y ) ( x — 2 y ) = 18 , ( x2 - 23 y ) 2 + ( x — 2 y ) = 7 . Examples of ...
... Solve the equation ( x2 + 5 ) 2 — 4 x2 = 160 . Ans . x 3 , or √ — 15 . 11. What two numbers are they , whose product is ... 23 y ) 3 + ( x2 — 23 y ) 2 + ( x2 — 23 y ) ( x — 2 y ) = 18 , ( x2 - 23 y ) 2 + ( x — 2 y ) = 7 . Examples of ...
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126 become zero 3d root arithmetical progression coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence