已知m>0,且m1/2+m(-1/2)=4,求[m3/2-m(-3/2)]/m1/2-m(-1/2)的值

Question

已知m>0,且m1/2+m(-1/2)=4,求[m3/2-m(-3/2)]/m1/2-m(-1/2)的值

Answer 1

m3/2-m(-3/2）=(m1/2)^3-m(-1/2)^3=(m1/2-m(-1/2)) (m+1+1/m) ----立方差公式
所以[m3/2-m(-3/2)]/m1/2-m(-1/2）=m+1+1/m=m+2+1/m-1=（m1/2+m(-1/2)）^2-1=16-1=15