Find all real number solutions for each equation. 4x^{3}=64x

Lorenzolaji

Lorenzolaji

Answered question

2021-11-17

Find all real number solutions for each equation.
4x3=64x

Answer & Explanation

Glenn Cooper

Glenn Cooper

Beginner2021-11-18Added 12 answers

Step 1
Given equation is 4x3=64x.
To find all real solution of the given equation.
Solution:
Given equation is 4x3=64x.
Solving the given equation.
4x3=64x
4x364x=0
4x(x216)=0
x(x216)=0
x(x+4)(x-4)=0 [Using a2b2=(a+b)(ab)]
x=0 or (x+4)=0 or x-4=0
x=0 or x=-4 or x=4
Step 2
Therefore, required solution is x={-4,0,4}.
Hence, solution of the given equation is x = {-4, 0 ,4}.
Novembruuo

Novembruuo

Beginner2021-11-19Added 26 answers

Calculation:
1)The given polynomial is 4x3=64x.
Set the above polynomial as an equation by equate withzero.
That is, 4x364x=0.
2)The common monomial factor available in the above equation is 4x.
So, the equation can be written as, 4x(x216)=0.
Therefore, 4x=0 or x216=0
3)The above equation x216=0 can be written as, x242=0.
Because, 42=44=16.
Since the above equation has 2 squares and they are subtracted, it represents the difference of two squares pattern. That is, a2b2=(a+b)(ab).
4)Now, we can apply the difference of two squares pattern to the above equation. Here, take x=a and 4=b.
Therefore, the equation can be written as follows:
(x+4)(x-4)=0
5)Hence the equation becomes,
x+4=0 or x-4=0.
Therefore, x=-4 or x=4.
Also, we have one more equation from step-2. That is, 4x=0.
Divide both sides of the equation by 4. Hence the equation becomes,
x=0.
So, the solution set is {-4,0,4}.
Final statement:
All the real number solutions for the given polynomial 4x3=64x are {-4, 0, 4}.

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