Question

Which system of equations can you use to find the roots of the equation? x3 – 10x = x2 – 6 y = x3 – x2 + 10x + 6 y = 0 y = x3 – x2 + 10x y = 6 y = x3 – 10x y = x2 – 6

Answer 1

The system of equations that can be used to find the roots of the equation ${x^3} - 10x = {x^2} - 6$ are $\boxed{y = {x^3} - 10x{\text{ and }}y = {x^2} - 6}$. Option (c) is correct.

Further explanation:

Given:

The equation is ${x^3} - 10x = {x^2} - 6.$

The options are as follows,

(a). $y = {x^3} - {x^2} + 10x + 6{\text{ and }}y = 0$

(b). $y = {x^3} - {x^2} + 10x {\text{ and }}y = 6$

(c). $y = {x^3} - 10x{\text{ and }}y = {x^2} - 6$

Explanation:

The given equation is ${x^3} - 10x = {x^2} - 6.$

The left hand side of the equation is ${x^3} - 10x.$

The right hand side of the equation is ${x^2} - 6.$

Consider the left hand side and right hand side as $y$.

$y = {x^2} - 6$ and $y = {x^3} - 10x$

Hence, option (c) is correct.

The system of equations that can be used to find the roots of the equation  are $\boxed{y = {x^3} - 10x{\text{ and }}y = {x^2} - 6}$. Option (c) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: system of equations, roots, equation, x3-10x = x2-6, zeros, find the roots.

Answer 2

Answer:

answer is:

$y=x^{3}-10 x,y=x^{2}-6$

Step-by-step explanation:

we are asked to find which system of equations can we use to find the roots of the equation:

$x^{3}-10x=x^{2}-6$

since the system of equation in last part is given as:

$y=x^{3}-10 x,y=x^{2}-6$

so, on equating both the equations i.e. on equating both the values of 'y' we get the desired equation as:

$x^{3}-10x=x^{2}-6$.