Find all values of x satisfying the given conditions: y=2x^3+x^2-8x+2 and y = 6

y2x3x2-8x2

#1

find all values of x satisfying the given conditions: y=2x^3+x^2-8x+2 and y = 6.

Answer:

putting the value of y in the 1st equation, we get
2x^3+x^2-8x-4=0
try putting x=-1, 1 to see if they satisfy the equation. They dont.
For solving cubic equations, first one needs to check if -2, -1, 1, 2 satisfy the equation.
In this case, -2 and 2 satisfy the equation. So, the answers are 2 and -2.

y=2x^3+x^2-8x+2 and y = 6
6=2x^3+x^2-8x+2
0=2x^3+x^2-8x-4
0=(2x^3+x^2)+(-8x-4)
0=x^2(2x+1)-4(2x+1)
0=(x^2-4)(2x+1)
0=(x-2)(x+2)(2x+1)
x=2,-2,-0.5
-0.5 however doesn’t fit into the equation properly, so, therefore, the final answers are -2 and 2.