Question

What are the roots of the polynomial equation `x^3-5x+5=2x^2-5`?

Answer 1

`x in {sqrt(5/2), -sqrt(5/2),2}`

Explanation:

`x^3-5x+5=2x^2-5`

`rArrcolor(white)("XX")x^3-2x^2-5x+10=0`

`rArrcolor(white)("XX")2x^2(x-2)-5(x-2)=0`

`rArrcolor(white)("XX")(2x^2-5)(x-2)=0`

`rArrcolor(white)("XX")2x^2-5=0color(white)("XX")rarrcolor(white)("XX")x=+-sqrt(5/2)`
or
`color(white)(rArr"XX")x-2=0color(white)("XXX")rarrcolor(white)("XX")x=2`