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

2 Answers
Apr 4, 2016

Answer:

#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

Answer:

#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#