please solve : X^3-6X+5=0

Question

Please solve step by step

Answer 1

By inspection we can see that X=1 is a root because 1-6+5=0.
Divide by X-1 using synthetic or algebraic division: X^2+X-5. We need the quadratic formula to solve this:
X=(-1±sqrt(21))/2=1.7913 or -2.7913.
So the solution is X=1,1.7913 or -2.7913.

Synthetic division
1 | 1 0 -6. 5
...| 1 1. 1 -5
...__________
.....1 1 -5| 0
(I've used dots as separators for clarity.)
i.e., X^2+X-5

Answer 2

Given: x³-6x+5
Notice that 6x=x+5x, so the equation can be restated as follows:

x³-6x+5=x³-x-5x+5=0 ⇒ x(x²-1)-5(x-1)=0 ⇒ x(x+1)(x-1)-5(x-1)=0 ⇒
(x-1){x(x+1)-5}=0 ⇒ (x-1)(x²+x-5)=0

Thus, we have: x-1=0 or x²+x-5=0
From x-1=0, we have: x=1   To evaluate x²+x-5=0, use the quadratic formula.
We have: x=(-1-sqrt(21))/2 or (-1+sqrt(21))/2

The answer : x=(-1-sqrt(21))/2, 1, or (-1+sqrt(21))/2