Answer:
i) The approximate solutions are: [tex]x_{1} \approx -0.207[/tex], [tex]x_{2} \approx 1.207[/tex].
ii) The approximate solutions are: [tex]x_{1}\approx -0.5[/tex], [tex]x_{2} \approx 1.5[/tex].
Step-by-step explanation:
i) The best approach to estimate graphically the solution of [tex]4\cdot x^{2} - 4\cdot x - 1 = 0[/tex] is graphing the following system of equations:
[tex]y = 4\cdot x^{2}-4\cdot x - 1[/tex] (1)
[tex]y = 0[/tex] (2)
And labeling the points in which both intersects each other. We include the result in the image 'solution-i'. The approximate solutions are: [tex]x_{1} \approx -0.207[/tex], [tex]x_{2} \approx 1.207[/tex].
ii) The best approach to estimate graphically the solution of [tex]4\cdot x^{2} - 4\cdot x - 1 = 2[/tex] is graphing the following system of equations:
[tex]y = 4\cdot x^{2}-4\cdot x - 1[/tex] (1)
[tex]y = 2[/tex] (2)
And labeling the points in which both intersects each other. We include the result in the image 'solution-ii'. The approximate solutions are: [tex]x_{1}\approx -0.5[/tex], [tex]x_{2} \approx 1.5[/tex].
