若a=根号2+1,b=根号2-1,则(-a²-b²/2ab)²*(-ab/a-b)²是有理数还是无理数
问题描述:
若a=根号2+1,b=根号2-1,则(-a²-b²/2ab)²*(-ab/a-b)²是有理数还是无理数
答
(-a²-b²/2ab)²×(-ab/a-b)²
=[(a²+b²)²/4a²b²]×(a²b²)/(a-b)²
=(a²+b²)²/4(a-b)²
=[(√2+1)²+(√2-1)²]²/4[√2+1-(√2-1)]²
=(2+2√2+1+2-2√2+1)²/4(√2+1-√2+1)²
=6²/4×2²
=36/16
=9/4
9/4是有理数