Question

A distância entre os pontos A ( 2b ,
- 3b) e B ( 6 , 4) é √91. Os possíveis valores de b é:​

Answer 1

$\large\boxed{\begin{array}{l}\sf x_B-x_A=6-2b\\\sf y_B-y_A=4-[-3b] =4+3b\\\sf d_{A, B}^2=(x_B-x_A)^2+(y_B-y_A)^2\\\sf (6-2b)^2+(4+3b)^2=(\sqrt{91}) ^2\\\sf 36-\diagdown\!\!\!\!\!\!24b+4b^2+16+\diagdown\!\!\!\!\!\!24b+9b^2=91\\\sf 13b^2+52=91\\\sf 13b^2=91-52\\\sf 13b^2=39\\\sf b^2=\dfrac{39}{13}\\\sf b^2=3\\\sf b=\pm\sqrt{3}\end{array}}$