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The sum of two positive integers is 97 and their difference is 37.
What is their product?

Sagot :

sqdancefan

Answer:

  2010

Step-by-step explanation:

If the numbers are x and y, you have ...

  x +y = 97

  x -y = 37

Adding these two equations gives ...

  2x = 134

  x = 67

  y = 67 -37 = 30

The product is then ...

  xy = (67)(30) = 2010

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Alternate solution

There is no need to find the actual numbers. We can go directly to their product.

  (x+y)² = x² +2xy +y² = 97² = 9409

  (x-y)² = x² -2xy +y² = 37² = 1369

Subtracting the second equation from the first gives ...

  4xy = 9409 -1369 = 8040

  xy = 8040/4 = 2010

Of course the difference of squares can be factored, so we could compute ...

  (97² -37²)/4 = (97 +37)(97 -37)/4 = 134(60)/4 = 134(15) = 2010

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