Question

(√3-√2)^2 - 2(1-√6) - (√3-√2) . (√3+√2)

a-0
b-1
c-2
d-3

Answer 1

Olá

$\mathsf{ (\sqrt{3} - \sqrt{2})^2~-~2(1- \sqrt{6} )~-~( \sqrt{3} - \sqrt{2} )\cdot( \sqrt{3} + \sqrt{2} ) }$

No primeiro termo, temos um produto notável

$\mathsf{\underbrace{(\mathsf{\sqrt{3} - \sqrt{2} })^2}_{(a-b)^2~=~(a^2-2ab+b^2)}~-~~2(1- \sqrt{6} )~-~( \sqrt{3} - \sqrt{2} )\cdot( \sqrt{3} + \sqrt{2} ) }$

Nos demais termos, aplica-se a distributiva

$\mathsf{ \underbrace{(\mathsf{( \sqrt{3})^2-2 \sqrt{6}+(\sqrt{2})^2 })}_{Produto ~ notavel}-(2- 2\sqrt{6} )-(( \sqrt{3})^2+ \sqrt{6}-\sqrt{6}~-(\sqrt{2})^2) }$

Cancela a raiz quadrada com o expoente 2.

$\mathsf{(\mathsf{3-2 \sqrt{6}+2 })-(2- 2\sqrt{6} )-( 3+ \diagup\!\!\!\!\! \!\sqrt{6}-\diagup\!\!\!\!\!\!\sqrt{6}~-2) }\\\\\\\mathsf{(\mathsf{5-2 \sqrt{6} })-(2- 2\sqrt{6} )-( 1) }\\\\\\\mathsf{5-~\diagup\!\!\!\!\!\!\!2 \sqrt{6} -2+~\diagup\!\!\!\!\!\!\!2 \sqrt{6}-1 }\\\\\\\boxed{\mathsf{2}}\qquad\qquad \Longrightarrow\text{Letra C)}$