SOLUTION: is it possible to write two real numbers whose sum is 4 and whose product is 5? use the quadratic formula to help explain, so far i have, x+y=4 (x)(y)=5

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: is it possible to write two real numbers whose sum is 4 and whose product is 5? use the quadratic formula to help explain, so far i have, x+y=4 (x)(y)=5      Log On


   

Question 747021: is it possible to write two real numbers whose sum is 4 and whose product is 5? use the quadratic formula to help explain,
so far i have,
x+y=4
(x)(y)=5
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
y=5%2Fx


%0D%0Ax%2B5%2Fx=5%0D%0A



%0D%0Ax%5E2%2B5=5x%0D%0A


%0D%0Ax%5E2-5x%2B5=0%0D%0A

this is clearly irreducible...so let's use the quadratic formula...


x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+


x+=+%285+%2B-+sqrt%28+5+%29%29%2F2+
So, yes if we extend our search out to all real numbers we can find two irrational numbers that meet our requirements

:)