Question

If 3x + 2y = 13 and xy = 6, find the value of 9x² + 4y².

Answer 1

Given: 3x + 2y = 13 and xy = 6

Step-wise calculation:

1. We want to find the value of 9x² + 4y².

2. Notice that (3x + 2y)² = 9x² + 12xy + 4y²

3. Substitute 3x + 2y = 13:

13² = 9x² + 12xy + 4y²

169 = 9x² + 12xy + 4y²

4. Now, substitute xy = 6: 

169 = 9x² + 12(6) + 4y² 

169 = 9x² + 72 + 4y²

5. Rearrange to isolate 9x² + 4y²:

9x² + 4y² = 169 – 72

9x² + 4y² = 97