已知:a≠b,且a的平方-2a-1=0,b的平方+2b-1=0,求a+1／b

题目

已知:a≠b,且a的平方-2a-1=0,b的平方+2b-1=0,求a+1／b
还有a/b的值?
不要求死算～

答案

由a^2 - 2a -1 = 0 得 （a - 1)^2 = 2,解得 a = 1 ± √2
由b^2 + 2b - 1 = 0 得 (b + 1)^2 = 2,解得 b = -1 ± √2
当 a = 1 + √2,b = - 1 + √2时,
a + 1/b = 1+√2 + 1/(-1+√2) = 2 + 2√2
a/b = (1+√2)/(-1+√2) = (1+√2)^1 = 3 + 2√2
当 a = 1 + √2,b = - 1 - √2时,
a + 1/b = 1+√2 + 1/(-1-√2) = 2
a/b =( 1 + √2)/(-1-√2) = -1
当 a = 1-√2,b = -1 + √2 时
a + 1/b = 1 - √2 + 1/(-1 +√2) = 1 - √2 + √2 +1 = 2
a/b = (1-√2)/(-1+√2) = -1
当 a= 1 - √2 b = -1 - √2 时
a + 1/b = 1 - √2 + 1/(-1 - √2) = 2 - 2√2
a/b = ( 1 - √2 ) / ( - 1 - √2 ) = 3 - 2√2