To solve the problem of finding two numbers that multiply to -48 and add to -2, follow these steps:
1. Understand the Problem:
- We need to find two numbers, say [tex]\( x \)[/tex] and [tex]\( y \)[/tex], such that:
- Their product [tex]\( x \cdot y = -48 \)[/tex]
- Their sum [tex]\( x + y = -2 \)[/tex]
2. List the Given Pairs:
- The provided pairs are:
1. (4, -12)
2. (3, -16)
3. (2, -24)
4. (1, -48)
5. (6, -8)
3. Check Each Pair:
- For each pair, we will check both the multiplication and addition conditions.
Check Pair 1: (4, -12)
- Product: [tex]\( 4 \cdot (-12) = -48 \)[/tex]
- Sum: [tex]\( 4 + (-12) = -8 \)[/tex]
- Conclusion: This pair does not satisfy the sum condition.
Check Pair 2: (3, -16)
- Product: [tex]\( 3 \cdot (-16) = -48 \)[/tex]
- Sum: [tex]\( 3 + (-16) = -13 \)[/tex]
- Conclusion: This pair does not satisfy the sum condition.
Check Pair 3: (2, -24)
- Product: [tex]\( 2 \cdot (-24) = -48 \)[/tex]
- Sum: [tex]\( 2 + (-24) = -22 \)[/tex]
- Conclusion: This pair does not satisfy the sum condition.
Check Pair 4: (1, -48)
- Product: [tex]\( 1 \cdot (-48) = -48 \)[/tex]
- Sum: [tex]\( 1 + (-48) = -47 \)[/tex]
- Conclusion: This pair does not satisfy the sum condition.
Check Pair 5: (6, -8)
- Product: [tex]\( 6 \cdot (-8) = -48 \)[/tex]
- Sum: [tex]\( 6 + (-8) = -2 \)[/tex]
- Conclusion: This pair satisfies both the multiplication and the addition conditions.
4. Conclusion:
- The pair (6, -8) is the correct solution. The numbers 6 and -8 multiply to -48 and add up to -2. Therefore, the numbers we are looking for are 6 and -8.
