x4次方+8x²-9因式分解--------------------已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15,则abc/ab+ac+bc=-------
问题描述：
x4次方+8x²-9因式分解--------------------已知1/a+1/b=1/6,1/b+1/c=1/9,1/a+1/c=1/15,则abc/ab+ac+bc=-------
答
1.x^4+8x^2-9=x^4-1+8x^2-8=(x^2+1)(x^2-1)+8(x^2-1)=(x+1)(x-1)(x^2+9)2.1/a+1/b=1/61/b+1/c=1/91/a+1/c=1/15三式相加得：2(1/a+1/b+1/c)=1/6+1/9+1/15=31/90即：1/a+1/b+1/c=31/180通分得：(ab+bc+ca)/(abc)=31/18...