SOLUTION: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers. I don't know how to start this problem. Also. 2x^2 + 6x + 3 = 0 how would you do this using c

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers. I don't know how to start this problem. Also. 2x^2 + 6x + 3 = 0 how would you do this using c      Log On


   

Question 185592This question is from textbook
: Two positive real numbers have a sum of 7 and a product of 11. Find the numbers.
I don't know how to start this problem.
Also. 2x^2 + 6x + 3 = 0
how would you do this using completing the square? I did it. but ended up with a weird answer like -3/2 +or- the square root of 3 over 2. This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two positive real numbers be x and y, then...
1) x%2By+=+7 "Two positive real numbers have a sum of 7..."
2) x%2Ay+=+11 "...and a product of 11."
Rewrite equation 1) as x = 7-y and substitute this for x in equation 2)
2a) %287-y%29%2Ay+=+11 Perform the indicated multiplication (distribute) on the left side.
2a) 7y-y%5E2+=+11 Rearrange to form a standard quadratic equation.
2a) y%5E2-7y%2B11+=+0 Use the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a to solve (a = 1, b = -7, c = 11):
x+=+%28-%28-7%29%2B-sqrt%28%28-7%29%5E2-4%281%29%2811%29%29%29%2F2%281%29 Simplify:
x+=+%287%2B-sqrt%2849-44%29%29%2F2
x+=+%287%2B-sqrt%285%29%29%2F2
highlight%28x+=+%287%2Bsqrt%285%29%29%2F2%29 or highlight%28x+=+%287-sqrt%285%29%29%2F2%29
Check:
= 14%2F2+=+7
%28%287%2Bsqrt%285%29%29%2F2%29%2A%28%287-sqrt%285%29%29%2F2%29+=+%2849-5%29%2F4 = 44%2F4+=+11
On part 2 of the problem, your "weird" answer is the correct solution!
highlight%28x+=+%28-3%2F2%29%2Bsqrt%283%29%2F2%29
highlight%28x+=+%28-3%2F2%29-sqrt%283%29%2F2%29