90th Problem 2016

We know that $(a+b)(a-b)=a^2-b^2$ .

$\left(3\sqrt{2}+\sqrt{5}\right)\left(3\sqrt{2}-\sqrt{5}\right)$

$\left(3\sqrt{2}\right)^2-\left(\sqrt{5}\right)^2$

$18-5=\boxed{13}$

$(3\sqrt{2} + \sqrt{5})(3\sqrt{2} - \sqrt{5}) = 3\sqrt{2}(3\sqrt{2} - \sqrt{5}) + \sqrt{5}(3\sqrt{2} - \sqrt{5}) = 9\sqrt{4 }-3\sqrt{10}+3\sqrt{10}-\sqrt{25}=18-5=$ $\boxed{13}$

Using identity a^2 - b^2 = (a + b)(a - b).

By solving we get,

= (3√2)^2 - (√5)^2

= 18 - 5

= 13.