问一道小升初的数学题.已知m[m(m＋n)＋n]＋n = 1,则m＋n的值是多少?
2019-05-30
问一道小升初的数学题.
已知m[m(m＋n)＋n]＋n = 1,则m＋n的值是多少?
优质解答
令m+n=t则n=t-m
m*(m*t+t-m)+t-m=1
m^2*t-m^2+m*t-m+t-1=0
m^2(t-1)+m(t-1)+t-1=0
(m^2+m+1)(t-1)=0
m^2+m+1=(m+1/2)^2+3/4>0
所以t-1=0,t=1即m+n=1
令m+n=t则n=t-m
m*(m*t+t-m)+t-m=1
m^2*t-m^2+m*t-m+t-1=0
m^2(t-1)+m(t-1)+t-1=0
(m^2+m+1)(t-1)=0
m^2+m+1=(m+1/2)^2+3/4>0
所以t-1=0,t=1即m+n=1