a+b=（4-2√2） （a+b）=2b 求b

a+b=（4-2√2） (a+b)=2b ==> a+b + 2ab = 2b ==> (4-2√2) + 2ab = 2b ==> 2 - √2 +ab = b ==> a = (b - 2 + √2) / b 将a = (b - 2 + √2) / b 代入 a+b=（4-2√2）中.==> [(b - 2 + √2) / b] + b = (4-2√2) ==> (b - 2 + √2) + b * b = (4-2√2)b ==> b^4 - (4 - 2√2)b + (2 - √2) + b^4 = (4-2√2)b ==> 2 b^4 - 2(4 - 2√2)b + (2 - √2) = 0 ==> b^4 - (4 - 2√2)b + (3 - 2√2) = 0 ==> b = { (4 - 2√2) ±√[(4 - 2√2) - 4 (3 - 2√2)]} / 2 ==> b = { (4 - 2√2) ±√[(24 -16√2) - (12 - 8√2)]} / 2 ==> b = { (4 - 2√2) ±√[24 -16√2 - 12 + 8√2 ]} / 2 ==> b = { (4 - 2√2) ±√[12 -8√2 ]} / 2 ==> b = { (4 - 2√2) ± 2√[3 -2√2 ]} / 2 ==> b = (2 - √2) ±√[3 -2√2 ] ==> b = (2 - √2) ±√[√2 - 1] ==> b = (2 - √2) ± [√2 - 1] ==> b = 1 or 3 - 2 √2