How do you solve 3x^4=375x?

2 Answers
Apr 4, 2016

x=5

Explanation:

This is an equation with a single variable, therefore we can reach its sollution through algebric operations. First, we must apply the same operation to both sides of the equation. Let's divide each by 3x:

(3x^4)/(3x)=(375x)/(3x)

On the left side, we will have x^3, because the division of powers with the same base is equals to the difference of the powers (4-1=3). The right side will be equals 125.

x^3=125
Finish by taking the cubic root of both sides of the equation:
x=root(3)125

x=5.

Apr 5, 2016

0,5,5(-1+-isqrt(3))/2

Explanation:

3x^4=375x

3x^4-375x=0

3x(x^3-125)=0

x=0 or x^3-125=0

The second expression as a trivial solution which is 5, but a third degree polynomial has tree roots (real or not).

Let's divide x^3-125 by x-5:

(x^3-125) / (x-5)=x^2+5x+25

so the equation is equivalent to:

x=0 or (x-5)(x^2+5x+25)=0

The second degree polynom has roots:

x=(-5+-sqrt(5^2-4*1*25))/2=(-5+-sqrt(25-100))/2

x=(-5+-sqrt(-75))/2=(-5+-5isqrt(3))/2=5(-1+-isqrt(3))/2