Question

$(3 \sqrt{2 } - 2 \div 3 \sqrt{2} + 2 )+ (3 \sqrt{2} + 2 \div 3 \sqrt{2} - 2)$
what is the answer

Answer 1

$\dfrac{3 \sqrt{2} - 2 }{ 3\sqrt{2} + 2} + \dfrac{3 \sqrt{2} + 2}{3 \sqrt{2} - 2 }$



$\dfrac{(3\sqrt{2}-2)(3\sqrt{2}-2) + (3\sqrt{2}+2)(3\sqrt{2}+2}{(3\sqrt{2}+2)(3\sqrt{2}-2)}$



$\dfrac{(3\sqrt{2}-2)^{2}+(3\sqrt{2}+2)^{2}}{(3\sqrt{2})^{2}-(2)^{2}}$



$\dfrac{(3\sqrt{2})^{2}+(2)^{2}-12\sqrt{2} + (3\sqrt{2})^{2}+(2)^{2} + 12\sqrt{2}}{18-4}$



$\dfrac{18+4+18+4}{16}$

$\dfrac{44}{14}$


22 / 7

π or 3.14

Answer 2

$\frac{3 \sqrt{2} - 2}{3 \sqrt{2} + 2 } + \frac{3 \sqrt{2} + 2}{3 \sqrt{2} - 2 } \\ = \frac{ {(3 \sqrt{2} - 2)}^{2} + {(3 \sqrt{2} + 2) }^{2} }{(3 \sqrt{2} + 2)(3 \sqrt{2} - 2) } \\ = \frac{18 + 4 - 12 \sqrt{2} + 18 + 4 + 12 \sqrt{2} }{ {(3 \sqrt{2}) }^{2} - {2}^{2} } \\ = \frac{22 + 22}{18 - 4} \\ = \frac{44}{14} \\ = \frac{22}{7} \\ = 3.142857142857142$