Solve {l}{a=0}{b=3+{(a+1)}sqrt{3}}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { a = 0 }\\ { b = 3 + {(a + 1)} \sqrt{3} }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for a, b, c, d

$$d=\sqrt{3}+3\approx 4.732050808$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$b=3+\left(0+1\right)\sqrt{3}$$

Add 0 and 1 to get 1.

$$b=3+1\sqrt{3}$$

Reorder the terms.

$$b=\sqrt{3}+3$$

Consider the third equation. Insert the known values of variables into the equation.

$$c=\sqrt{3}+3$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$d=\sqrt{3}+3$$

The system is now solved.

$$a=0 b=\sqrt{3}+3 c=\sqrt{3}+3 d=\sqrt{3}+3$$