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

Guest Jul 25, 2019

#1**+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 \(y_1\cdot y_2\cdot y_3\cdot y_4\cdot =0\cdot 0\cdot 0\cdot 0=0\)

!

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 \(8\cdot 5,0902\cdot (-7)\cdot (-6,0902)=\color{blue}1736,02\)

!

asinus Jul 25, 2019