x>0,依三元均值不等式得
x²+(1/2x)
＝x²+1/(4x)+1/(4x)
≥3·[x²·1/(4x)·1/(4x)]^(1/3)
＝(3/4)·4^(1/3).
取等时,
x²＝1/(4x)→x＝(1/2)·2^(1/3).
故所求最小值为：(3/4)·4^(1/3).