https://file.aiquickdraw.com/mathbot/file/1726957502413clycs66c.jpg

The image shows a pattern puzzle with "Y" shaped branches, and the objective is to find the missing value in the third "Y."

Let's analyze the pattern:

1. **First Y**:
   - Top values: 3, 2
   - Bottom value: 25

2. **Second Y**:
   - Top values: 4, 3
   - Bottom value: 49

3. **Third Y**:
   - Top values: 9, 8
   - Bottom value: ?

### Analysis of the Pattern:
Looking at the first two "Y" figures:
- For the first Y:
  \( 3^2 + 2^2 = 9 + 4 = 13 \)
  - Multiply by 2: \( 13 \times 2 = 26 \), but subtract 1 to get 25.

- For the second Y:
  \( 4^2 + 3^2 = 16 + 9 = 25 \)
  - Multiply by 2: \( 25 \times 2 = 50 \), but subtract 1 to get 49.

### For the third Y:
- \( 9^2 + 8^2 = 81 + 64 = 145 \)
  - Multiply by 2: \( 145 \times 2 = 290 \), but subtract 1 to get 289.

However, none of the options match this logic. The reasoning pattern here seems to follow a simpler rule as the correct pattern would likely yield 50 from the squared sum leading us to **option (b)**.



Find the missing value in the Y-shaped branches where the first two figures show (3, 2) = 25 and (4, 3) = 49, and the third figure has (9, 8) with a missing value.

Solve this Y-shaped pattern puzzle by analyzing the squared sums of given values. Explore the logical reasoning used to find the missing value, focusing on exponentiation and arithmetic operations. Suitable for Grades 5-7.

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