A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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Page 10
... sides the square of the coefficient of x . Then 4 × 172x2 + 4 × 17 × 19x + 192 = 4 × 17 × 1848 + 192 = 126025 ; .. 2 × 17x + 19 = ± 355 , + 355-19 x = = 91 , or — II . 34 48 . x + ( x2 − ax + b2 ) * = x2 + 6 ; - α • ° • ( x2 — ax + b3 ) ...
... sides the square of the coefficient of x . Then 4 × 172x2 + 4 × 17 × 19x + 192 = 4 × 17 × 1848 + 192 = 126025 ; .. 2 × 17x + 19 = ± 355 , + 355-19 x = = 91 , or — II . 34 48 . x + ( x2 − ax + b2 ) * = x2 + 6 ; - α • ° • ( x2 — ax + b3 ) ...
Page 15
... sides , and complete the square , 2 I x2 a2 ( x2 — — 1 ) 2 + 40c2 .. ac2 - 4 - 4 4 + = a2 - -4a2 = = a2 ( 1 − a1 ) ; I 9 . ~ / 2 = 22 ( − 1 ± √ I− a1 ) . ха a2 Whence x = -1 ± ( 1 − a1 ) * ± Ex . 41 . - { 2 ± 2 ( 1 − a1 ) * } * j ...
... sides , and complete the square , 2 I x2 a2 ( x2 — — 1 ) 2 + 40c2 .. ac2 - 4 - 4 4 + = a2 - -4a2 = = a2 ( 1 − a1 ) ; I 9 . ~ / 2 = 22 ( − 1 ± √ I− a1 ) . ха a2 Whence x = -1 ± ( 1 − a1 ) * ± Ex . 41 . - { 2 ± 2 ( 1 − a1 ) * } * j ...
Page 26
... sides from 4 , we get ≈2 + 332-162 3 * 2 - 33 % +90 - = 223 22- IIZ + 18 · 6 ) ( ≈ — 27 ) _ 3 ( ≈ — 5 ) ( ≈ − 6 ) ; 222 = - ( ≈ − 2 ) ( ≈ −9 ) Whence -6 = 0 ; .. 2 = 6 ; . * . x = 54-6 × 5 = 2 ; y = 3 . 2 × 6 65 . x + y ...
... sides from 4 , we get ≈2 + 332-162 3 * 2 - 33 % +90 - = 223 22- IIZ + 18 · 6 ) ( ≈ — 27 ) _ 3 ( ≈ — 5 ) ( ≈ − 6 ) ; 222 = - ( ≈ − 2 ) ( ≈ −9 ) Whence -6 = 0 ; .. 2 = 6 ; . * . x = 54-6 × 5 = 2 ; y = 3 . 2 × 6 65 . x + y ...
Page 27
... + y = the hypothenuse , and x - yone side . = Then by the question , 4xy 2 ............ .. . ( 1 ) , and 4 { ( x + y ) 2 + ( x − y ) 2 } = 5 { ( x + y ) + ( x − y ) } .... ( 2 ) , - from ( 1 ) , ( 4xy ) * = SIMULTANEOUS EQUATIONS . 27.
... + y = the hypothenuse , and x - yone side . = Then by the question , 4xy 2 ............ .. . ( 1 ) , and 4 { ( x + y ) 2 + ( x − y ) 2 } = 5 { ( x + y ) + ( x − y ) } .... ( 2 ) , - from ( 1 ) , ( 4xy ) * = SIMULTANEOUS EQUATIONS . 27.
Page 28
... side , ( 4xy ) = √2 , the other side . Let x , y , z be the numbers . 18 Then x + y + z = 26 ............. x2 + y2 + z2 = 300 x2 — y2 = y2 — z3 ....... From ( 2 ) , x— 2y2 + z2 = 0 ; • . 3y2 = 300 ; :: y = 10 , x2 + 22 = 200 , x + z = ...
... side , ( 4xy ) = √2 , the other side . Let x , y , z be the numbers . 18 Then x + y + z = 26 ............. x2 + y2 + z2 = 300 x2 — y2 = y2 — z3 ....... From ( 2 ) , x— 2y2 + z2 = 0 ; • . 3y2 = 300 ; :: y = 10 , x2 + 22 = 200 , x + z = ...
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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