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Question

Accepted Answer

Let us denote y = x + 1/(9x) = 3. We are to find the value of 9x^2 + 1/(9x^2).

Step 1: Express 9x^2 + 1/(9x^2) in terms of x + 1/(9x).
Let A = x + 1/(9x) = 3.

Step 2: Find x^2 + 1/(81x^2):
(x + 1/(9x))^2 = x^2 + 2 * x * 1/(9x) + 1/(81x^2)
= x^2 + 2/9 + 1/(81x^2)

So,
x^2 + 1/(81x^2) = (x + 1/(9x))^2 - 2/9
= 3^2 - 2/9 = 9 - 2/9 = (81 - 2)/9 = 79/9

Step 3: Find 9x^2 + 1/(9x^2):
Multiply both sides by 9:
9x^2 + 1/(9x^2) = 9 * (x^2 + 1/(81x^2))
= 9 * (79/9) = 79

Final Answer: 79

Answer

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