The numerical equation from Qin Jiushao’s Shushu jiuzhang analyzed in...

20.  The numerical equation from Qin Jiushao’s Shushu jiuzhang analyzed in Section 7.4.2 came from the geometrical problem of finding the area of a pointed field. If the sides and one diagonal are labelled as in Figure 7.22 (shown below)

-- Show that the area of the lower triangle is given by: B = (c/2) sqrt(b2 - (c/2)2) and that of the upper triangle by: A = (c/2) sqrt(a2 - (c/2)2) then the area x of the entire field is given by x = A + B.
-- Show that x satisfies the fourth-degree polynomial equation x4 + 2(A2+ B2)x2 - (A2 - B2)2 = 0. If a = 39, b = 20, and c = 30, show that this equation becomes the one solved by Qin in the text.