Given that 3t - (1 / 3t) = 3, which of the following expressions has the value equal to 12?

Question

Accepted Answer

Step 1: Given 3t - (1 / 3t) = 3.

Step 2: Let x = 3t - (1 / 3t) = 3.

Step 3: Square both sides:  
(x)^2 = 3^2  
=> (3t - 1/(3t))^2 = 9

Step 4: Expand the left side:  
(3t)^2 - 2 * 3t * (1/(3t)) + (1/(3t))^2 = 9  
=> 9t^2 - 2 + 1/(9t^2) = 9

Step 5: Rearrange:  
9t^2 + 1/(9t^2) - 2 = 9

Step 6: Add 2 to both sides:  
9t^2 + 1/(9t^2) = 11

Step 7: Now check the options:   
Option 1: 9t^2 + 1/(9t^2) + 2 = 11 + 2 = 13 (Not 12)   
Option 2: 9t^2 + 1/(9t^2) - 2 = 11 - 2 = 9 (Not 12)  
Option 3: 9t^2 + 1/(9t^2) + 1 = 11 + 1 = 12 (Correct)   
Option 4: 9t^2 + 1/(9t^2) = 11 (Not 12)

Therefore, the expression with value equal to 12 is option 3: 9t² + (1 / 9t²) + 1.

Answer

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