Question 857283
For a+x, b+x, c+x to form a geometric sequence, we must have *[tex \large (b+x)^2 = (a+x)(c+x) \Rightarrow x^2 + 2bx + b^2 = x^2 + (a+c)x + ac]. Subtract x^2 from both sides and you will obtain *[tex \large b^2 - ac = (a+c-2b)x \Rightarrow x = \frac{b^2 - ac}{a+c-2b}], provided this number exists.