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The sum of two prime numbers is 85. What is the product of these two prime numbers?

The answer is 166.

Sagot :

To find the two prime numbers given their sum and product:

The sum of two distinct prime numbers is 85.
x + y = 85
y = 85 - x

Representation:
Let the first prime number be x
The other prime number be 85 - x

The product of the prime numbers is 166.
(x) (85-x) = 166
-x² + 85x = 166

Transform to quadratic equation, ax² +bx = c = 0
-x² + 85x - 166 = 0

Solve by factoring or using quadratic formula.  Since the equation can be factored, solve by factoring:

-1(-x² + 85x - 166 = 0)-1
x² - 85x + 166 = 0
(x - 83) (x-2) = 0

x - 83 = 0           x - 2 = 0
x = 83   x = 2

The two prime numbers are 83 and 2.

To check:

83 + 2 = 85
(83) (2) = 166


                  
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