Factorise ÷ then split
X³-6x+4
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Answer:
How do I solve x^3 - 6x + 4= 0?
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x^3 – 6x + 4 = 0
Let us consider the expression, x^3 -6x +4
We are going to use the trial and error method to factorise this expression,
Let us consider the value of x to e 1.
When x = 1
(1)^3 – 6(1) + 4
= 1 – 6 + 4
= -1
Therefore, x = 1 is not the required value.
When x = 2
(2)^3 – 6(2) + 4
= 8 -12 + 4
= 12 – 12
= 0
Therefore, the value of the expression becomes 0 when the value of x is equal to 2.
Hence, (x-2) is a factor.
Now,
X^3 – 6x + 4
= x^3 – 2x^2 +2x^2 – 4x -2x +4
= x^2(x-2) +2x(x-2) -2(x-2)
= (x-2)(x^2 +2x -2)
Therefore the given equation can also be written as,
(x-2)(x^2 + 2x - 2) = 0
Since, the product of two expressions is 0, then the value of either of the expression must be 0.
Therefore, x-2 = 0
x = 2
Again, x^2 +2x – 2 = 0
Using Sridharacharya’s rule for solving quadratic equation we get,
x = -1 + i
x = -1 – i
Therefore,
x = 2, -1 + i, -1 -i
Step-by-step explanation:
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