先化简再求值1.当a=1+√2,b=1-√2时,求(1÷a-b-1÷a+b)÷b÷a²-2ab+b²的值
问题描述:
先化简再求值1.当a=1+√2,b=1-√2时,求(1÷a-b-1÷a+b)÷b÷a²-2ab+b²的值
答
你是不是想问(1÷(a-b)-1÷(a+b))÷b÷(a²-2ab+b²)的值,1÷(a-b)-1÷(a+b))=2b/[(a+b)(a-b)]=2b/(a²-b²)
a²-2ab+b²=(a-b)² a+b=2,a-b=2√2就能算了
答
(1÷a-b-1÷a+b)÷b÷a²-2ab+b²
=(2b/[(a-b)(a+b)]÷[b÷(a-b)²]
=2b(a-b)²/[b(a-b)(a+b)]
=2(a-b)/(a+b)
=4√2/2
=2√2