Question

calcule o numero real a de forma que a distância do ponto P(2a,3) ao ponto Q(1,0) seja igual 3 raiz de 2.

Answer 1

$\sqrt{(1-2a)^2+(0-3)^2}=3 \sqrt{2}\\ \sqrt{1^2-2\cdot1\cdot2a+(2a)^2+(-3)^2}=3 \sqrt{2}\\ \sqrt{4a^2-4a+1+9}=3 \sqrt{2}\\ \sqrt{4a^2-4a+10}=3 \sqrt{2}\\ ( \sqrt{4a^2-4a+10})^2=(3 \sqrt{2})^2\\ 4a^2-4a+10=18\\ 4a^2-4a-8=0~~(divide~por~4)\\ a^2-a-2=0\\\\ a_1=-1~~e~~a_2=2$