Question

A distância do ponto A(a,1) ao ponto B(0,2) é igual a 5. Determine o valor da abscissa a.

Answer 1

5²=1²+x²
25=1+x²
25-1=x²
24=x²
x=√24

Answer 2

$d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\5=\sqrt{(0-a)^2+(2-1)^2}\\\\5=\sqrt{a^2+1}\\\\(\sqrt{a^2+1})^2=(5)^2\\\\a^2+1=25\\\\a^2=24\\\\a=\sqrt{4\cdot6}\\\\\boxed{a=2\sqrt{6}}$