Question

B is the midpoint of AC. AB=x^ 2 . BC=4x+5 Find AC

Answer 1

Answer:

AC = 50

Step-by-step explanation:

Since, B is the midpoint of AC.

$\therefore AB = BC\\\therefore x^2 = 4x + 5\\\therefore x^2 - 4x - 5 =0\\\therefore x^2 - 5x + x - 5= 0\\\therefore x(x - 5) +1(x - 5)=0\\\therefore (x - 5)(x + 1) =0\\\therefore x - 5 = 0\: or \: x + 1 = 0\\\therefore x = 5 \: or \: x = - 1\\ \because x = - 1 \: doesn't \: satisfy\: the\: \\condition \: of \: midpoint \\ \therefore x =5\\\because AC = AB + BC\\\therefore AC = x^2 + 4x + 5\\\therefore AC = x^2 + 4x + 5 \\\therefore AC = 5^2 + 4\times 5 + 5\\\therefore AC = 25 + 20 +5\\\huge \red {\boxed {\therefore AC = 50}}$