Solve {r}{a=sqrt{3}(2+sqrt{3})+1}{b=4+3sqrt{2}}

$$\left. \begin{array} { r } { a = \sqrt { 3 } ( 2 + \sqrt { 3 } ) + 1 } \\ { b = 4 + 3 \sqrt { 2 } } \end{array} \right.$$

Solve for a, b

$$a=2\left(\sqrt{3}+2\right)\approx 7.464101615$$

$$b=3\sqrt{2}+4\approx 8.242640687$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \sqrt{3} by 2+\sqrt{3}.

$$a=2\sqrt{3}+\left(\sqrt{3}\right)^{2}+1$$

The square of \sqrt{3} is 3.

$$a=2\sqrt{3}+3+1$$

Add 3 and 1 to get 4.

$$a=2\sqrt{3}+4$$

The system is now solved.

$$a=2\sqrt{3}+4 b=4+3\sqrt{2}$$