We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
78
1
avatar

Find the product of the $y$-coordinates of all the distinct solutions $(x,y)$ for the two equations $y=x^2-8$ and $y^2=-5x+44$.

 Jul 25, 2019
 #1
avatar+8521 
+1

Find the product of the $y$-coordinates of all the distinct solutions $(x,y)$ for the two equations $y=x^2-8$ and $y^2=-5x+44$.

 

Hello Guest!

 

\(y=x^2-8\\ y^2=-5x+44 \).

\(y^2=x^4-16x^2+64\)

\(x^4-16x^2+64=-5x+44\\ x^4-16x^2+5x+20=0\)

http://www.arndt-bruenner.de/mathe

\(x_4=3,618\\ x_3=1,382\\ x_2=-1\\ x_1=-4\\ y_{1,2,3,4}=0\)

 

The product of the y-coordinates is \(y_1\cdot y_2\cdot y_3\cdot y_4\cdot =0\cdot 0\cdot 0\cdot 0=0\)

laugh  !

That was a wrong consideration. Sorry.
I correct.

\(f(x)=y=x^2-8\\ g(x)=y =\pm\sqrt{-5x+44}\)

http://www.arndt-bruenner.de/mathe/

\(P_1(-4/8)\\ P_2(3,618/5,0902)\\ P_3(-1/-7)\\ P_4(1,382/-6,0902)\)

 

The product of the y-coordinates is \(8\cdot 5,0902\cdot (-7)\cdot (-6,0902)=\color{blue}1736,02\)

laugh  !

 Jul 25, 2019
edited by asinus  Jul 25, 2019

8 Online Users

avatar