簡單迭代方程求解

1.
7(7(7(7(7(7(3x - 3) - 3) - 3) - 3) - 3) - 3) - 3 = 3x/7
i.e.
3x/7 = 3x - 3
x = 7x - 7
-6x = -7
x = 7/6

2.
20/(12 + 20/(12 + 20/(12 + x))) = x
i.e.
x = 20/(12 + x)
x(12 + x) = 20
x^2 + 12x - 20 = 0
(x + 6)^2 = 20 + 36 = 56
x + 6 = +/- 2(14)^(1/2)
x = -6 +/- 2(14)^(1/2)

1. 7(7(7(7(7(7(3x–3)–3)–3)–3)–3)–3)–3 = 3x/7
2470629x–2882397 = 3x
x=823543x-960799
823542x=960799
x=1/1/6
=1.17(to 3 sig fig)