use the analytic method to solve the equation,

Question

1. use the analytic method to solve the equation,

(2x+5)^1/2-3=(x-2)^1/2

 

2. In a manufacturing operated, the cost, c is related to the manufacturing time, t by the equation c= square root of t. find the extact value of c when t =200

Answer 1

1. √(2x+5) - 3 = √(x-2)

 

    Square both sides:  2x+5 - 6√(2x+5) + 9 = x-2

 

    Isolate the remaining radical term:  -6√(2x+5) = -16-x

 

    Square both sides and simplify:  36(2x+5) = 256+32x+x²

 

                                                 72x + 180 = 256 + 32x + x²

 

                                                  x² - 40x + 76 = 0

 

                                                 (x-38)(x-2) = 0

 

                                                  x = 38 or x = 2

 

Substitute each value into the ORIGINAL equation.  They both satisfy the equation, so the solutions are 38 and 2.

 

2. c(t) = √t

 

   c(200) = √200 = √100√2 = 10√2