53/37=1+1/（x+1/（y+1/z））,求x+y+z=?.

Question

53/37=1+1/（x+1/（y+1/z））,求x+y+z=?.

Answer 1

53/37=1+1/（x+1/（y+1/z））
53/37
=1+16/37
=1+1/(37/16)
=1+1/(2+5/16)
=1+1/(2+1/(16/5))
=1+1/(2+1/(3+1/5))
则对应x=2 y=3 z=5
x+y+z=2+3+5=10