Diamond Problem Solver
Solve diamond math problems. Find two numbers given their sum and product.
PRODUCT
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SUM
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Try:
How to Use
- Choose whether to find numbers or find sum/product
- Enter the known values in the diamond
- Click "Solve Diamond"
- View the solution with verification
What is Diamond Problem Solver?
A diamond problem is a math puzzle where you find two numbers given their sum and product, or vice versa. The numbers are placed on the left and right of a diamond shape, with their product at the top and sum at the bottom.
Formula
To find two numbers from sum (S) and product (P):
Solve: x² - Sx + P = 0
Using quadratic formula: x = (S ± √(S²-4P)) / 2
Examples
- Sum=7, Product=12: Numbers are 3 and 4
- Sum=5, Product=6: Numbers are 2 and 3
- Sum=-1, Product=-12: Numbers are 3 and -4
- Numbers 5 and 6: Sum=11, Product=30
FAQ
What if there's no solution?
Some sum and product combinations have no real number solutions. This happens when the discriminant (S²-4P) is negative. For example, sum=2 and product=5 has no real solutions.
Can diamond problems have negative numbers?
Yes! If the product is negative, one number must be positive and one negative. If the product is positive but sum is negative, both numbers are negative.
How are diamond problems useful in algebra?
Diamond problems help with factoring quadratics. To factor x²+bx+c, you need two numbers that multiply to c and add to b - exactly what diamond problems train you to find!
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