History of Hindu Mathematics: A Source Book v2.c17.s9.35

v2.c17.s9.35

$4√(x/2) + 8√(1/10(x - 4√(x/2)))$ $+ 9√(½(x - 4√(x/2)) - 8√(1/10(x - 4√(x/2))))$ $+ 56 = x.$ Put y = x - 4√(x/2); then $y - 8√(y/10) - 9√((y - 8√(y/10))/2) = 56.$ Again put z = y - 8√(y/10); then $z - 9√(z/2) = 56.$ Therefore z = ((9 + √(81 + 4.2.56))/2)² × ½ = 128. Then y - 8√(y/10) = 128; whence y = ((8 + √(64 + 10.4.128))/2)² × 1/10 = 160. Again x - 4√(x/2) = 160; hence x = ((4 + √(16 + 4.2.160))/2)² × ½ = 200.