Explore a wide range of topics and get answers from experts on IDNLearn.com. Get the information you need from our community of experts, who provide detailed and trustworthy answers.
Sagot :
[tex]\begin{cases} y=3x-20 \\ y=-x^2+34 \end{cases}\\ \\ \begin{cases} y=3x-20 \\3x-20=-x^2+34 \end{cases}\\ \\\begin{cases} y=3x-20 \\x^2+3x-20-34=0 \end{cases}\\ \\\begin{cases} y=3x-20 \\x^2+3x-54=0 \end{cases}[/tex]
[tex]\begin{cases} y=3x-20 \\x^2+3x-54=0 \end{cases} \\ \\x^2+3x-54=0 \\ \\a=1, \ \ b=3, \ \ c= -54 \\ \\ \Delta =b^2 -4ac =3^2-4*1*(-54)=9+216=225 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-3-\sqrt{225}}{2}=\frac{-3-15}{2}= \frac{-18}{2}=-9[/tex]
[tex]x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{-3+\sqrt{225}}{2}=\frac{-3+15}{2}= \frac{12}{2}=6[/tex]
[tex]\begin{cases} y=3x-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3x-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=3*(-9)-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3*6-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-27-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=18-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-47 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=-2\\x=6 \end{cases}[/tex]
[tex]\begin{cases} y=3x-20 \\x^2+3x-54=0 \end{cases} \\ \\x^2+3x-54=0 \\ \\a=1, \ \ b=3, \ \ c= -54 \\ \\ \Delta =b^2 -4ac =3^2-4*1*(-54)=9+216=225 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-3-\sqrt{225}}{2}=\frac{-3-15}{2}= \frac{-18}{2}=-9[/tex]
[tex]x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{-3+\sqrt{225}}{2}=\frac{-3+15}{2}= \frac{12}{2}=6[/tex]
[tex]\begin{cases} y=3x-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3x-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=3*(-9)-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3*6-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-27-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=18-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-47 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=-2\\x=6 \end{cases}[/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.