a²+ab-b²=0
a²+ab+ b²/4- b²/4-b²=0
(a+ b/2)²- 5b²/4=0
(a+ b/2-√5b/2) (a+ b/2+√5b/2)=0
a=(√5-1)b/2或a=(-√5-1)b/2
a/b=(√5-1)/2或a/b=(-√5-1)/2(舍去,a,b均为正数)
(a²-b²)/(b-a)(b-2a)+(2a²-ab)/(4a²-4ab+b²）*(2a+b)/(2a-b)
=(a+b)(a-b)/(b-a)(b-2a)+[a(2a-b)/(2a-b)²]*(2a+b)/(2a-b)
=(a+b)(a-b)/(a-b)(2a-b)+[a(2a-b)/(2a-b)²]*(2a+b)/(2a-b)
=(a+b)/(2a-b)+a(2a+b)/(2a-b)²
=[(a+b)(2a-b)+a(2a+b)]/(2a-b)²
=(2a²+ab-b²+2a²+ab)/(2a-b)²
=(4a²+2ab-b²)/(2a-b)²
=(4a²-4ab+b²+6ab-2b²)/(2a-b)²
=[(2a²+b²)+2(a²+ab-b²)]/(2a-b)²
=(2a²+b²)/(2a-b)²
=(2a²+b²)/(4a²-4ab+b²）（分子分母同除以b²）
=[2(a/b)²+1]/[4(a/b)²-4(a/b)+1]
将a/b=(√5-1)/2代入,得
原式=[2(a/b)²+1]/[4(a/b)²-4(a/b)+1]
={2[(√5-1)/2])²+1]}/{4[(√5-1)/2])²-4*(√5-1)/2+1}
={2*(6-2√5)/4+1}/{4*(6-2√5)/4-2√5+2+1}
=[3-√5+1]/[6-2√5-2√5+3]
=[4-√5]/[9-4√5]
=(4-√5)(9+4√5)/(9-4√5)(9+4√5)
=36+16√5-9√5-20
=16+7√5