Question

Fie punctele A(-a; 5) şi B(0; -3). Valorile numărului real a pentru care AB = 10 sunt egale cu ​

Answer 1

 

$\displaystyle\bf\\AB=\sqrt{(0-(-a))^2+(-3-5)^2}\\\\AB=\sqrt{a^2+(-8)^2}\\\\AB=\sqrt{a^2+8^2}\\\\AB=\sqrt{a^2+64}\\\\\sqrt{a^2+64}=10~~\Big|^2\\\\a^2+64=100\\\\a^2=100-64\\\\a^2=36~~\Big|~\sqrt{~~}\\\\a=\pm6\\\\\boxed{\bf a_1=6~~si~~a_2=-6}$