+1904 $${\mathtt{y}} = \left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,\times\,}}\left({\left({\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}^{{\mathtt{2}}}\right)$$ and $${\mathtt{y}} = {\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}$$
+128407 y = (x + 2)(x - 2)^2 y = 3x + 5 setting the y's equal, we have
(x + 2) (x - 2)^2 = 3x + 5 simplify
(x + 2) (x - 2) ( x - 2) = 3x + 5
(x^2 - 4)(x - 2) = 3x + 5
x^3 - 4x - 2x^2 + 8 = 3x + 5
x^3 - 2x^2 - 7x + 3 = 0 this isn't capable of being factored and the Rational Roots Theorem doesn't produce any results. either.......thus....a graphical solution seems to be a good option.....here you are....
https://www.desmos.com/calculator/x6n42ipgpu
The solutions are (approximately) x = -2.074, .393 and 3.68
And here are the approximate points of intersection of the original equations
https://www.desmos.com/calculator/8ltpkas08e
(-2.074, -1.221), (.393, 6.179), (.368, 16.041)
+128407 y = (x + 2)(x - 2)^2 y = 3x + 5 setting the y's equal, we have
(x + 2) (x - 2)^2 = 3x + 5 simplify
(x + 2) (x - 2) ( x - 2) = 3x + 5
(x^2 - 4)(x - 2) = 3x + 5
x^3 - 4x - 2x^2 + 8 = 3x + 5
x^3 - 2x^2 - 7x + 3 = 0 this isn't capable of being factored and the Rational Roots Theorem doesn't produce any results. either.......thus....a graphical solution seems to be a good option.....here you are....
https://www.desmos.com/calculator/x6n42ipgpu
The solutions are (approximately) x = -2.074, .393 and 3.68
And here are the approximate points of intersection of the original equations
https://www.desmos.com/calculator/8ltpkas08e
(-2.074, -1.221), (.393, 6.179), (.368, 16.041)
