Question

The equation align="absmiddle" class="latex-formula"> has solutions of the form
M= N +or- sqaure root of D/over M


Solve this equation and find the appropriate values of N,M,and D. Do not worry about simplifying the √D portion of the solution.


N= M= D=

Answer 1

Answer:

• N = 1
• M = 4
• D = 65

Step-by-step explanation:

The given equation is of the form ...

  ax² +bx +c = 0

where a=2, b=-1, c=-8.

The quadratic formula gives the solution to the above equation as ...

  $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

So, for your equation, the solution is ...

  $m=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(-8)}}{2(2)}=\dfrac{1\pm\sqrt{65}}{4}$

Comparing this to the form ...

  $m=\dfrac{N\pm\sqrt{D}}{M}$

we see ...

• N = 1
• M = 4
• D = 65