Question

已知2x+4y=1求证:x的平方+y的平方大于等于1/20

Answer 1

y=(1-2x)/4

x²+y²

=x²+(1-4x+4x²)/16

=(20x²-4x+1)/16

=[20(x-1/10)²+4/5]/16

20(x-1/10)²+4/5≥4/5

所以[20(x-1/10)²+4/5]/16≥(4/5)/16=1/20

所以x²+y²≥1/20