Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Find two real numbers whose sum is 34.5 and whose product is 297

Sagot :

AL2006
x + y = 34.5
xy = 297
From the first one . . . y = 34.5 - x
Plug that into the second one . . . x(34.5 - x) = 297
Eliminate parentheses . . . 34.5x - x² = 297
Bend that around and tidy it up . . . x² - 34.5x + 297 = 0
Apply the quadratic formula to that, and find . . .
x =18
x = 16.5
kate200468
[tex] \left \{ {\big{x+y=34.5} \atop \big{xy=297}} \right.\\\\ \left \{ {\big{x=34.5-y\ \ \ \ \ } \atop\big {(34.5-y)y=297}} \right.\\\\\\ 34.5y-y^2-297=0\ \ \ \Rightarrow\ \ \ -y^2+34.5y-297=0\ /\cdot 2\\\\-2y^2+69y-594=0\\\\ \ \ \ \Rightarrow\ \ \ \Delta=69^2-4\cdot(-2)\cdot(-594)=4761-4752=9\\\\y_1= \frac{-69-3}{2\cdot(-2)} = \frac{-72}{-4} =18\ \ \ \Rightarrow\ \ \ x_1=34.5-18=16.5\\\\y_2= \frac{-69+3}{2\cdot(-2)} = \frac{-66}{-4} =16.5\ \ \ \Rightarrow\ \ \ x_2=34.5-16.5=18[/tex]

[tex]Ans.\ two\ numbers\ are:\ 18\ \ \ and\ \ \ 16.5[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.