If a, b, c are real numbers, then the intervals in which fx =x+a2abacab      x+b2 bcacbc       x+c2  is strictly  decreasing

f(x)=1abcax+a2ab2ac2a2bbx+b2bc2a2cb2ccx+c2=abcabcx+a2b2c2a2x+b2c2a2b2x+c2=x+a2+b2+c2b2c2x+a2+b2+c2x+b2c2x+a2+b2+c2b2x+c2=x+a2+b2+c21b2c21x+b2c21b2x+c2=x2x+a2+b2+c2f′(x)=3x2+2xa2+b2+c2f′(x)<0x(3x+2)a2+b2+c2≤0−23a2+b2+c2≤x≤0x(3x+2)≤0−23≤x≤0