Respuesta :
Answer:
answer is:
[tex]y=x^{3}-10 x,y=x^{2}-6[/tex]
Step-by-step explanation:
we are asked to find which system of equations can we use to find the roots of the equation:
[tex]x^{3}-10x=x^{2}-6[/tex]
since the system of equation in last part is given as:
[tex]y=x^{3}-10 x,y=x^{2}-6[/tex]
so, on equating both the equations i.e. on equating both the values of 'y' we get the desired equation as:
[tex]x^{3}-10x=x^{2}-6[/tex].
The system of equations that can be used to find the roots of the equation [tex]{x^3} - 10x = {x^2} - 6[/tex] are [tex]\boxed{y = {x^3} - 10x{\text{ and }}y = {x^2} - 6}[/tex]. Option (c) is correct.
Further explanation:
Given:
The equation is [tex]{x^3} - 10x = {x^2} - 6.[/tex]
The options are as follows,
(a). [tex]y = {x^3} - {x^2} + 10x + 6{\text{ and }}y = 0[/tex]
(b). [tex]y = {x^3} - {x^2} + 10x {\text{ and }}y = 6[/tex]
(c). [tex]y = {x^3} - 10x{\text{ and }}y = {x^2} - 6[/tex]
Explanation:
The given equation is [tex]{x^3} - 10x = {x^2} - 6.[/tex]
The left hand side of the equation is [tex]{x^3} - 10x.[/tex]
The right hand side of the equation is [tex]{x^2} - 6.[/tex]
Consider the left hand side and right hand side as [tex]y[/tex].
[tex]y = {x^2} - 6[/tex] and [tex]y = {x^3} - 10x[/tex]
Hence, option (c) is correct.
The system of equations that can be used to find the roots of the equation are [tex]\boxed{y = {x^3} - 10x{\text{ and }}y = {x^2} - 6}[/tex]. 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.
