Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals 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 appreciate your time. Please revisit us for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.