A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 72
... transformed 15 . equation . 2 + 0-13 + 10 - 19 - + 2 + 2 – II – 2 + 2 - II - I - I 1 - 20 +2 + 4-7 2 + 4 7 + 2 + 6 8 2 + 6 - Ι +2 2 + 8 • ' . 2y + + 8y3 — y2 - 8y - 200 is the transformed equation . Ex . 5 . 1. Transform the equation ...
... transformed 15 . equation . 2 + 0-13 + 10 - 19 - + 2 + 2 – II – 2 + 2 - II - I - I 1 - 20 +2 + 4-7 2 + 4 7 + 2 + 6 8 2 + 6 - Ι +2 2 + 8 • ' . 2y + + 8y3 — y2 - 8y - 200 is the transformed equation . Ex . 5 . 1. Transform the equation ...
Page 73
... transformed equation are to be those of the original , increased cach by 15 3 + 15 + 25-3 9 or 5 ; thus 50 125 5- 3 9 3+ 10+ 3 - 25 152 152 9 .. 3y3 - 25 " 9 is the required equation . or 27y3 - 152 = 0 5- 3 3+ 5+ 0 -5 3 + 0 14. To take ...
... transformed equation are to be those of the original , increased cach by 15 3 + 15 + 25-3 9 or 5 ; thus 50 125 5- 3 9 3+ 10+ 3 - 25 152 152 9 .. 3y3 - 25 " 9 is the required equation . or 27y3 - 152 = 0 5- 3 3+ 5+ 0 -5 3 + 0 14. To take ...
Page 74
... transformed equation , which by the process in ( 14 ) is found to be 27y ++ 67y — 59 = 0 . 19. Let m = 1 , and a , b , c ...... l , be the n roots . - Then — n ( n − 1 ) k2 + ( n − 1 ) pk + q = 0 , N - I nk + p = 0 . 22 + q = 0 ...
... transformed equation , which by the process in ( 14 ) is found to be 27y ++ 67y — 59 = 0 . 19. Let m = 1 , and a , b , c ...... l , be the n roots . - Then — n ( n − 1 ) k2 + ( n − 1 ) pk + q = 0 , N - I nk + p = 0 . 22 + q = 0 ...
Page 75
... transformed equation be ́y3 — Qy + R = 0 , - then if a , b , c be the roots of the proposed equation , Q = ( a + b ) ... transformed equation is x3 - 40x - 39 = 0 . Ex . 8 . 2. Let x3- Px2 + Qx SYMMETRICAL FUNCTIONS . 75.
... transformed equation be ́y3 — Qy + R = 0 , - then if a , b , c be the roots of the proposed equation , Q = ( a + b ) ... transformed equation is x3 - 40x - 39 = 0 . Ex . 8 . 2. Let x3- Px2 + Qx SYMMETRICAL FUNCTIONS . 75.
Page 76
... transformed equation , then ( 1 ) P = ab + ac + bc = q , = Q = ab.ac + ab . bc + ac . bca ( abc ) + b ( abc ) + c ( abc ) = abc ( a + b + c ) = pr , Rab.ac.bc = a2b2c2 = r2 ; therefore the transformed equation is - x3- qx2 + prx — r2 ...
... transformed equation , then ( 1 ) P = ab + ac + bc = q , = Q = ab.ac + ab . bc + ac . bca ( abc ) + b ( abc ) + c ( abc ) = abc ( a + b + c ) = pr , Rab.ac.bc = a2b2c2 = r2 ; therefore the transformed equation is - x3- qx2 + prx — r2 ...
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A Companion to Wrigley's Collection of Examples: Being Illustrations of ... John Thompson Platts,Alfred Wrigley No preview available - 2016 |
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a+b+c a²+b² a²b³ AB² ABCD AC² angle ABC axis BC² beam centre of gravity chord circle co-ordinates coefficient cos² cos³ cosec² curve diameter draw ellipse equal equilateral Eucl Hence hyperbola Join latus rectum Let ABC middle point MULTINOMIAL THEOREMS parabola parallel perpendicular plane point of contact point of intersection r₁ radius required locus right angle roots S₁ sec² segment sides Similarly sin² sin³ square straight line tan² tangent term transformed equation triangle ABC values vertical weight whence X₁