Deuces wild

Algebra Level pending

We have two equations with two unknowns one of which is of degree 2.

Let $C$ and $D$ be positive real numbers such that the following equations both hold true:

(I) $C^2 = 27D$

(II) $C + D = 73$

Find $D$ to 3 decimal places.

1 solution

Denton Young
Oct 30, 2017

Since $C + D = 73$ , $C = 73 - D$

Substituting, $(73 - D)^2 = 27D$

Simplifying, $D^2 - 173D + 5329 = 0$

Use the quadratic formula and discard the extraneous solution.