Find the product of the $y$-coordinates of all the distinct solutions $(x,y)$ for the two equations $y=x^2-8$ and $y^2=-5x+44$.
+14915 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 \(8\cdot 5,0902\cdot (-7)\cdot (-6,0902)=\color{blue}1736,02\)
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