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某些物理问题。往往牵涉到两个物理变量之间的关系,利用绝对值不等式定理来求解,显得方便简捷。定理:①若a、b为任意两正数,并且a+b=定值,则其乘积ab仅当a=b时为极大;②若a、b为任意正数,并且ab=定值,则其和a+b仅当a=b时为极小。下面举例说明: 例1、如图1电路,证明:当R=r时,电源输出功率最大。 [证]∵U+U_r=ε为定值。由定理①可知,U=U_r时,即IR=Ir,或R=r时,U·U_r,有极大值。
Some physical problems. The relationship between two physical variables is often involved, and the absolute value inequality theorem is used to solve it, which is convenient and simple. Theorem: 1 If a, b are any two positive numbers, and a + b = fixed value, then its product ab is only great when a = b; 2 if a, b is any positive number, and ab = fixed value , and its a + b is only minimal when a = b. The following example illustrates: Example 1, as shown in Figure 1, the circuit proves: When R = r, the power output power is maximum. [Certificate] ∵ U+U_r=ε is a fixed value. According to Theorem 1, when U=U_r, ie, IR=Ir, or R=r, U·U_r has a maximum value.