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7 is the right answer.
Step-by-step explanation:
First write down the value of a and 1/a and then start to rationalize the denominator if 1/a to get the exact value of 1/a and then we get 3-root5/2 and then now with the found values of a and 1/a start to find the value of 1/a+a and then we can find the value of their square easily by Squaring the both sides of the equation.squaring we are using the basic algebraic identity of a+b whole square and then by cacelling the terms of 2ab we get the solution of a square +1/a square here and then 9-2 in the right hand side now solving it we get 7 as the result.
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