Verified answer

solve

acx^2-b(c+a)x+(c+a)^2=0

x = (a + c)(b ± √(b^2 - 4ac))/(2ac) =

= [(a + c)/c](b ± √(b^2 - 4ac))/(2a)

roots are

x_1 = [(a + c)/(ac)]·α

x_2 = [(a + c)/(ac)]·β

express (a + c)/(ac) = 1/a + 1/c

in terms of α and β

remember these relations

α + β = - b/a

α · β = c/a