In each of these questions two equations 1 and 2 are given.You have to solve both the equations and give answer
(A) if `a lt b`
(B) if `a gt b`
( C ) if relationship between a and b cannot been established
(D) if `a ge b`
(E) if `a le b`
(1) `a^2 =4`
(2) `b^2 = 9`

Answer

To solve the given problem, we need to analyze the two equations provided:

1. \( a^2 = 4 \)
2. \( b^2 = 9 \)

### Step 1: Solve the first equation \( a^2 = 4 \)

To find the values of \( a \), we take the square root of both sides:

\[ a = \sqrt{4} \quad \text{or} \quad a = -\sqrt{4} \]

This gives us:

\[ a = 2 \quad \text{or} \quad a = -2 \]

### Step 2: Solve the second equation \( b^2 = 9 \)

Similarly, we take the square root of both sides:

\[ b = \sqrt{9} \quad \text{or} \quad b = -\sqrt{9} \]

This gives us:

\[ b = 3 \quad \text{or} \quad b = -3 \]

### Step 3: Compare the values of \( a \) and \( b \)

Now we have the possible values for \( a \) and \( b \):

- For \( a \): \( 2 \) and \( -2 \)
- For \( b \): \( 3 \) and \( -3 \)

We need to compare these values:

1. If \( a = 2 \):
- \( 2 < 3 \) (so \( a < b \))
- \( 2 > -3 \) (so \( a > b \))

2. If \( a = -2 \):
- \( -2 < 3 \) (so \( a < b \))
- \( -2 > -3 \) (so \( a > b \))

### Step 4: Establish the relationship

From the comparisons:
- When \( a = 2 \), \( a < b \) when \( b = 3 \).
- When \( a = -2 \), \( a > b \) when \( b = -3 \).

Since we have different relationships depending on the values of \( a \) and \( b \), we cannot establish a consistent relationship between \( a \) and \( b \).

### Conclusion:

Since the relationship between \( a \) and \( b \) cannot be established consistently, the answer is:

**(C) if the relationship between a and b cannot be established.**

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