Question

已知m平方-1=m,n平方-1=n,求m平方+n平方的值.

Answer 1

m²-1=m,则m²-m=1,则m²-m+1/4=5/4,则,(m-1/2)²=5/4,则m-1/2=±√5/2,则m=1/2±√5/2

∵n²-1=n,同理可得,n=1/2±√5/2

∵m²=(1/2±√5/2)²=1/4±√5/2+5/4=3/2±√5/2

n²=(1/2±√5/2)²=1/4±√5/2+5/4=3/2±√5/2

又∵√5≈2.236 ...=0,n²>=0,而3/2-√5/2