若x>0时,函数y=ax方+1/x的最小值为3,则正实数a= 5
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利用均值不等式:
a1 + a2 + ... + an >= n * (a1 * a2 * ... * an)^(1/n);
其中a1, a2, ..., an为正实数,当且仅当a1=a2=...=an时取等号。
y = ax^2 + 1/x = ax^2 + 1/2x + 1/2x >= 3(ax^2 * 1/2x * 1/2x)^(1/3) = 3 * (a/4)^(1/3) = 3
==> (a/4)^(1/3) = 1
==> a/4 = 1
==> a = 4
a1 + a2 + ... + an >= n * (a1 * a2 * ... * an)^(1/n);
其中a1, a2, ..., an为正实数,当且仅当a1=a2=...=an时取等号。
y = ax^2 + 1/x = ax^2 + 1/2x + 1/2x >= 3(ax^2 * 1/2x * 1/2x)^(1/3) = 3 * (a/4)^(1/3) = 3
==> (a/4)^(1/3) = 1
==> a/4 = 1
==> a = 4
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