Page 45 - WCS - Electrical
P. 45

WORKSHOP CALCULATION & SCIENCE  - CITS



           7   3x y  ÷ -6x y
                  2 3
                         5
 m+
   m   m  x a a x   x  a = a a m+ n n       2 3x y 2 2 3  3 y 3  2  2 y 2
 n
   m n
 n m+
 n a =
 =
 a
 a
 a
                  3x
                           y
              = == = 3x 5  y 5 =  = y =  3 2x 3
                   −
                    6x y
                       y
                  −
   m   m a = m− m− n n  − 6x 6x 5 y 2x 2x 3
 a
   m
 a
 m−
 n
 a
 a
 =
 a n a n a n  = a  8  3x y  ÷ xy
                  3 2
                  3x  3x y 3 3 2  2 y 2  2  2
                  3
 m.
 n m.
   m n
   m a ] =  a a n m. n n    =  =                          y3x== 3x xy y =  3x 3x y 2 y
                =
                        =
 a
 n =
 a [
                    xy
   m ][ ] =
 a
                 xy
 [
           9   Divide 45a b c by 9a c
                         2 2
                                  2

 m
   1/m
   1/m  m  m a       45a 45a b 2 b c 2 c
                           2
                      2
                        2 2
 a
   1/m = a=
 a
 a
 a
 =
               = =  = = 45a  2 b  c
                      2
                      9a c
                    9a 9a 2 c
                         c
    −   m − m 1  1
 m =
 a    a =  =  1 m  =5b 2
 −
 a
 a m a a m
           Algebraic Formulae
   1   1 =  a = m a m
 m
   1
                                          2
                    2
                                      2
 m
 m
 a − a − a − m  = a  1  (a + b)     =   a  + b  + 2ab
           2  (a - b) 2       =      a  + b  - 2ab
                                          2
                                      2

    m / m /  nn m   2                     2
 n m
 n
 a
 a    a m /= n = a n m  3  (a + b)      =   (a - b)  + 4ab
 =
 a
 a
           4  (a - b)         =      (a + b) -4ab ; (a + b)2-(a - b) =4ab
                                                              2
                   2
                                           2
 2
   3x + 22y 2y 2 2  5  a  + b       =   (a + b)  - 2 ab = (a - b)2 + 2 ab
 2
   2
 2y
   3x +
                   2
                                           2
 3x +
               2
 2
 2
 2
 2 +
 3y
 2x 3y+
 2x 2x + 3y 2 2
                   2
               2
 _______
 _______   6  a  - b          =      (a + b) (a - b)
 _______
 2
 2
 2
 5y
 x + 2 x + 5y 2 2  7  a  + b       =   (a + b) (a  + b  - ab)
 5y
                   2
               2
                                                 2
                                             2
 x +
 _______
 _______
 _______
           8  a  - b          =      (a - b) (a  + b  + ab)
                   3
               3
                                             2
                                                 2
           9  (a + b)         =      a  + b  + 3ab (a + b)
                    3
                                          3
                                      3
   12  x 12x y 3 3 2 y = 2 3xy 3xy  10 (a - b) 3  =  a  - b  - 3ab (a - b)
   3
 2 y
 12x
                                      3
                                          3
 =
 2
 2
 4x y
 4x 4x 2 y  =  3xy  11 (a + b + c) 2  =  a  + b  + c  + 2 (ab + bc + ca)
 y
                                          2
                                      2
                                              2
           12 a  - b 4        =      (a  + b ) (a + b) (a - b)
                                           2
                                       2
               4
 15
   15  y 15y 15 y = 10 y 10  Examples
   15
 10
 15y
 =
 5
 15y 15y 5 5  =  y  1   If x + y = 9 and xy = 20
 15y
                                                2
                                                   2
                         2
                             2
   3a   3a  x  2  x  4a  x  5a 3 3     Find   i) x  + y    ii) x - y  iii) x  - y
  2
 3
  x
 5a
 4a
 2  x  5a x 4a
 3a
                              3
                                        3
                          3
                                            3
 4
 4
 10a
 6a 6a 4  x  10a        iv) x  + y    v) x  - y    vi) x and y
 6a 10a x
  x
               i       (a + b) =     a  + b  + 2ab
                             2
                                      2
                                          2

      60a 60a 6 6        (x + y)   =   x  + y  + 2xy
 6
                                          2
                                      2
                            2
 =  = = 60a = 5 a = = a a
 5
                                      2
                                          2
 60a 60a 5             (9) 2  =      x  + y  + 2 (20)
 60a
                       81     =      x  + y  + 40
                                          2
                                      2
 15
      25a−    − 25a 15  x  + y   =   81 - 40
 15
                        2
                            2
 =  = = − 25a − 8
 −
                        2
 −
 5a
                            2
 − 5a 5a 8 − 8         x  + y   =    41
 −
               ii      (a - b)   =   (a + b)  - 4ab
                                           2
                            2
 2
      4x  4x y 2 y  2  2
   2
 4x
 2x
 2x
 =  = = 2y 2y = y = 2x 2        (x - y)   =   (x + y)  - 4xy
                                           2
                            2
 =
 2y
                              =      (9)   - 4 (20)
                                       2
                              =      81 - 80
                                                           32
                                            CITS : WCS - Electrical - Exercise 4
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