Question

30 PONTOS (URGENTE!!!) As retas de equações (-√2+k)x-y=-2 e √2 x+y=1 são perpendiculares entre si. O valor de k é igual a: *
a) (3√2)/2
b) √2
c) -2
d) 4
e) 102

Answer 1

Resposta:

$-\frac{\sqrt{2}}{2}$

Explicação passo a passo:

$Para\ ser\ perpendicular\ m_1\bullet{m_2}=-1\\\\m_1=-(\sqrt{2+k})\\\\m_2=\sqrt{2} \\\\\\-(\sqrt{2+k})\bullet\sqrt{2}=-1\\\\-(\sqrt{4}+k\sqrt{2})=-1\\\\(\sqrt{4}+k\sqrt{2})=1\\\\2+k\sqrt{2}=1\\\\k\sqrt{2}=1-2\\\\k\sqrt{2}=-1\\\\k=-\frac{1}{\sqrt{2}}=-\frac{1}{\sqrt{2}}\bullet\frac{\sqrt{2}}{\sqrt{2}}=-\frac{\sqrt{2}}{2}$