Question

Which system of equations can be used to find the roots of the equation 12x3-5x=2x2+x+6

Answer 1

`y = 12 {x}^(3) - 5x`

{

`y= 2 {x}^(2) + x + 6`

EXPLANATION

The given equation is

`12 {x}^(3) - 5x = 2 {x}^(2) + x + 6`

To find the system of equations, we just have to equate each side of the equation to y and form two different equations.

The left sides gives one equation,

`y = 12 {x}^(3) - 5x`

The right side also gives,

`y= 2 {x}^(2) + x + 6`

Hence the correct choice is A

Answer 2

A
`\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.`

Explanation:

The equation
`12x^3-5x=2x^2+x+6` have in both sides expressions
`12x^3-5x` and
`2x^2+x+6.`

Therefore, the system of two equations

`\left\{\begin{array}{l}y=12x^3-5x\\ \\y=2x^2+x+6\end{array}\right.`

has the solution (x,y), where x is the solution of the equation above.