Question

qual é o valor de x-y, sabendo que x+y=7e x²-y²=42?

Answer 1

Qual é o valor de x-y, sabendo que x+y=7e x²-y²=42


TEMOS QUE ACHAR O VALOR DE
(x) e de ( y)

{x + y = 7
{ x² - y² = 42


x + y = 7 ---------------------isolar o (x)
x = 7 - y    ------------------substituir o (x)

x² - y² = 42
(7-y)² - y² = 42 ---------------------fazer a distributiva
(7-y)(7-y) - y² = 42
(49 - 7y-7y+ y²) - y² = 42
49 - 14y + y² -y² = 42
49 - 14y       0     = 42
49 - 14y = 42
- 14y = 42 - 49
- 14y = - 7
y = - 7/-14
y = + 7/14-----------------------------divide AMBOS  por 7
y = 1/2
(ACHAR o valor de (x))

x = 7 - y
               1
x = 7 - ------
              2
       2(7) - 1
x = --------------                                verificando  para
             2                                         x = 13/2   e  y = 1/2
       14 - 1
x = ------------                                    x + y = 7 
           2                                           13   1
                                                       ----+----= 7
         13                                            2     2
x = ---------
           2                                                14  
                                                             ---- = 7
V = { 13/2 ; 1/2}                                     2
                                                              7 = 7


Qual é o valor de x-y?                           x² - y² = 42
para                                                    (13/2)² - (1/2)² = 42
x = 13/2                                               (13²/2²) - (1²/2²) = 42
y = 1/2                                                 169/4    - 1/4      = 42
                                                             169         1 
13       1                                                 ------ - -------     = 42
----- - ------ =                                            4           4
2          2                      
  13 - 1                                                           168       
--------------   =                                                 -----    =   42
        2                                                                4            

12                                                                      42 = 42
---- = 6
  2             

então x - y = 6