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Start by calculating the value of x.
What two rational numbers have a product of - 12 and a sum of 4?
Start by calculating the value of y.
What two rational numbers have a product of - 56 and a sum of - 1?
Example Graph:
Example Graph:
Let's take a look at the diagram and the pattern!
y= 1.2
LHS-1.2=RHS-1.2
1.2-1.2=0
a-b = a+(- b)
Add terms
We want to complete the given Diamond Problem. Let's consider the given diagram and the pattern used in the problem!
We can fill the remaining corners when we find two rational numbers that sum up to 4 and have a product of - 12. To find these numbers, let's think of different pairs of numbers that we can multiply to get - 12 and calculate their sums till we find the pair that sums up to 4.
| Product (xy) | Sum (x+y) | Is Sum Equal to 4? |
|---|---|---|
| - 12=1(- 12) | 1+(- 12) =- 11 | * |
| - 12=2(- 6) | 2+(- 6)=- 4 | * |
| - 12=3(- 4) | 3+(- 4)=- 1 | * |
| - 12=4(- 3) | 4+(- 3)=1 | * |
| - 12=6(- 2) | 6+(- 2)=4 | ✓ |
Notice that we can complete our pattern when one factor is equal to 6 and the other is equal to - 2. Let's complete our Diamond Problem!
Remember that this is one of the possible solutions. The Diamond Problem with x=- 2 and y=6 also corresponds to the pattern.
Let's take a look at the diagram and the pattern!
Let's start by analyzing the given diagram and the pattern used in the problem!
We can fill the remaining corners when we find two rational numbers that sum up to - 1 and have a product of - 56. To find these numbers, let's think of different pairs of numbers that we can multiply to get - 56 and calculate their sums till we find the pair that sums up to - 1.
| Product (xy) | Sum (x+y) | Is Sum Equal to - 1? |
|---|---|---|
| - 56=1(- 56) | 1+(- 56)=- 55 | * |
| - 56=2(- 28) | 2+(- 28)=- 26 | * |
| - 56=4(- 14) | 4+(- 14)=- 10 | * |
| - 56=7(- 8) | 7+(- 8)=- 1 | ✓ |
Notice that 7 and - 8 are the numbers for which the product is - 56 and the sum is - 1. We can use this information to fill our Diamond Problem.
Remember that this is one of the possible solutions. The Diamond Problem for x=- 8 and y=7 also corresponds to the pattern.
