已知a/b=c/d求证(1)a-2b/b=c-2d/b (2)a²+2b²/a²=c²+2d²/c²
问题描述:
已知a/b=c/d求证(1)a-2b/b=c-2d/b (2)a²+2b²/a²=c²+2d²/c²
答
设a/b=c/d,则a=tb,c=td,所以a-2b/b=(tb-2b)/b=t-2,c-2d/d=(td-2d)/d=t-2,所以a-2b/b=c-2d/bd;(2)a²+2b²/a²=(tb)²+2b²/(tb)² =t²+2/t² ,c²+2d²/c² ==(td)...