ElectricPavlov

sqrt (24) = x^2+x^2

sqrt 24 = 2 x^2       square both sides

24 = 4 x^4

6 = x^4

x = 1.5650845800732873

Yah....didn't see the little dot above the 6 ...I am more accustomed to a bar...though I have seen the dot before...

Hooray !......if I ever need to call Germany....  I would likely just use Wi-Fi calling for free...

See below:

(-k)^2  - 4 (k-5)(5)   = 0

k^2 - 20k + +100 = 0

(k-10)(k-10) = 0       k= 10   or  10       (so really, only ONE solution)

   Are they ALSO asking for the solution to the ORIGINAL equation when k = 10  maybe ?????

Hey Melody.... I didn't round...... the diff was my mistake  using  Kaylee's 10 year balance for 40 years  ( SHOULD be  39)  ....should have re-read the Q ! 

Using the Quadratic Formula   \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

you'll find there are TWO values of 'x'  that satisfy this quadrtatic     x  =  4 +- sqrt(15)   

     sub each of these x values in the   x + 1/x    equation              <=====     Take it from here !

The 'discriminant' is the     b^2 - 4ac      portion of the Quadratic Formula:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

a = k-5     b = -k       c = 5 

When the discriminat = 0   there is only one solution to the quadratic        

(-k)^2  - 4 (k-5)(5)   = 0      <======== can you take it from here....solve for k ?

Wilma    (x-1)(x-8) = x^2 - 9x + 8       and  8 is correct

Greg      (x-1)(x+4) = x^2 + 3x -4       and  3 is correct

 then the correct   =   x^2 + 3x + 8          use quadratic formula    x = -3/2  +- sqrt (23)i / 2

    =    1.07305 x 10⁵  ~~ 1.07 x 10⁵   units/hr          for 3 significant digits