Question

\left |\begin{array}{ccc}2+√3 & 3+√11\\ 3-√11 &2-√3\end{array}\right | ,Evaluate it

Answer 1

Answer:

$\left |\begin{array}{ccc}2+\sqrt3& 3+\sqrt{11}\\3-\sqrt{11}&2-\sqrt3\end{array}\right|=3$

Step-by-step explanation:

$\left |\begin{array}{ccc}2+\sqrt3& 3+\sqrt{11}\\3-\sqrt{11}&2-\sqrt3\end{array}\right|$

$=(2+\sqrt3)(2-\sqrt3)-(3+\sqrt{11})(3-\sqrt{11})$

using

$\boxed{(a+b)(a-b)=a^2-b^2}$

$=(2^2-{\sqrt3}^2)-(3^2-{\sqrt{11}}^2)$

$=(4-3)-(9-11)$

$=1-(-2)$

$=1+2$

$=3$

$\implies\:\boxed{\left |\begin{array}{ccc}2+\sqrt3& 3+\sqrt{11}\\3-\sqrt{11}&2-\sqrt3\end{array}\right|=3}$