SOLUTION: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers.

Question 407134: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose that x and y are the numbers, such that x + y = 7 and xy = 11. Two ways to solve this:

Solution 1:
Substitute y = 7 - x into the second equation to obtain x(7 - x) = 11. Now you can find x using the quadratic formula.

Solution 2: Assume that x and y are roots of a polynomial of the form . Applying Viete's formulas, the sum of the roots of the polynomial is -b, and the product is c, so we have

. The roots of z are the values of x and y. Note that this is the same quadratic as in the previous solution.
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