Question

帮忙……已知x1小于x2,判断根号下x1^2+1 - 根号下x2^2+1 +x2-x1是大于0还是小于0

Answer 1

x1,x2应该都要大于0吧

记a1=(x1^2+1)^0.5

a2=(x2^2+1)^0.5

a2^2-a1^2=x2^2-x1^2

a1-a2+x2-x1=x2-x1-(a2^2-a1^2)/(a2+a1)=x2-x1-(x^2^2-x1^2)/(a1+a2)

a1>x1,a2>x2（x2^2-x1^2)/(a1+a2)