<PRE><B>Question 1206122</B>
&lt;br&gt;
The given equation is {{{a+1/3a=2}}}.&lt;br&gt;
Square both sides of the equation:&lt;br&gt;
{{{(a+1/3a)^2=2^2}}}
{{{a^2+2/3+1/9a^2=4}}}&lt;br&gt;
Note that the middle term when squaring the left side of the equation is a constant; it contains no variables.  That is the key to solving a problem like this.&lt;br&gt;
{{{a^2+1/9a^2=4-2/3=10/3}}}&lt;br&gt;
Multiply both sides of the equation by 9 to get the expression we want:&lt;br&gt;
{{{9a^2+1/a^2=9(10/3)=30}}}&lt;br&gt;
ANSWER: 30&lt;br&gt;
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