If `a = (1)/(a)= m and a ne 0`, find in terms of 'm', the value of :
`a^(2) - (1)/(a^(2))`

Answer

To solve the problem, we start with the given information:

1. We have \( a = m \) and \( \frac{1}{a} = m \).
2. We need to find the value of \( a^2 - \frac{1}{a^2} \) in terms of \( m \).

### Step-by-step Solution:

**Step 1: Express \( a \) and \( \frac{1}{a} \) in terms of \( m \)**

From the problem, we know:
\[ a = m \quad \text{and} \quad \frac{1}{a} = m \]

**Step 2: Find \( a^2 \) and \( \frac{1}{a^2} \)**

Now, we calculate \( a^2 \) and \( \frac{1}{a^2} \):
\[ a^2 = (m)^2 = m^2 \]
\[ \frac{1}{a^2} = \left(\frac{1}{m}\right)^2 = \frac{1}{m^2} \]

**Step 3: Substitute into the expression \( a^2 - \frac{1}{a^2} \)**

Now, we substitute \( a^2 \) and \( \frac{1}{a^2} \) into the expression:
\[ a^2 - \frac{1}{a^2} = m^2 - \frac{1}{m^2} \]

**Step 4: Simplify the expression**

To simplify \( m^2 - \frac{1}{m^2} \), we can find a common denominator:
\[ m^2 - \frac{1}{m^2} = \frac{m^4 - 1}{m^2} \]

Thus, the final expression in terms of \( m \) is:
\[ a^2 - \frac{1}{a^2} = \frac{m^4 - 1}{m^2} \]

### Final Answer:
\[ a^2 - \frac{1}{a^2} = \frac{m^4 - 1}{m^2} \]

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