Question

Multiply and find the product $(\frac{3}{2}+\sqrt{5})(\frac{3}{2}-\sqrt{5})$.

Answer 1

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

$(a+b)(a-b)=a^2-b^2$

$\Rightarrow {\left(\frac{3}{2}\right)}^2-(\sqrt{5}{)}^2=\frac{9}{4}-5$

$=\frac{9-20}{4}=\frac{-11}{4}$.