Answer:
Explanation:
An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.
See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.
I show you that in the attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.
The intersection point is (0,0) meaning that the solution is x = 0, y = 0.
The system of equations are [tex]\boxed{y = 4{x^2}}{\text{ and }}\boxed{y = {x^3} + 2x}[/tex] that can be used to find the roots of the equation [tex]4{x^2} = {x^3} + 2x.[/tex]
Further explanation:
Given:
The equation is [tex]4{x^2} = {x^3} + 2x.[/tex]
Explanation:
The given equation is [tex]4{x^2} = {x^3} + 2x.[/tex]
Consider the left hand side of the equation [tex]4{x^2} = {x^3} + 2x[/tex].as y and the right hand side of the equation [tex]4{x^2} = {x^3} + 2x[/tex] as y.
[tex]\begin{aligned}y&= 4{x^2} \hfill\\y&= {x^3} + 2x \hfill\\\end{aligned}[/tex]
To obtain the roots of the system of equation we have to solve the equations.
The system of equations are [tex]\boxed{y = 4{x^2}}{\text{ and }}\boxed{y = {x^3} + 2x}[/tex] that can be used to find the roots of the equation [tex]4{x^2} = {x^3} + 2x.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomials
Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations, [tex]4x2 = x3 + 2x[/tex], roots, roots of equation.
