Solve the equation x^4+81=3831. Find the exact answer in simplified radical form.

Answer 1

x⁴ + 81 = 3831

x⁴ = 3750

x⁴ = (625)(6)

x = ±5(⁴√6)

Answer 2

Firstly, rearrange the equation to isolate X⁴:

X⁴ + 81 - 81 = 3831 - 81

X⁴ = 3750

Next factor 3750, two factors are 625 and 6

therefore X⁴ = 625 x 6, and this can be simplified:

X⁴ = 5 x 5 x 5 x 5 x 6

X⁴ = 5⁴ x 6 and then taking the 4th root of each side gives two solutions:

X = +5 ∜6 and -5 ∜6

Answer 3

You want to isolate the variables so you can have easier time to square root the variables so to do that subtract the 81 from both sides. So, it will look like this

x⁴ + 81 = 3821

- 81 - 81

x^{4 =} 3740

Now this next step you can do both ways because it will give you 2 answers. You keep the +3740 on one side or subtract and then subtract -x⁴ because both ways will give the answer. It will look like this.

x⁴ - 3740 = 0

-x⁴ -x⁴

-3740 = - x⁴

So, in this step we will square root the -x⁴ or the x⁴ and -3740 or 3740 by 4, since you are solving for x. This, will look like this.

∜(-3740)⁼ ∜(-x⁴)

Now, since you can square root negative numbers place a -1 out side each parentheses and solve. It will look like this.

(-1)∜(3740) ⁼ ∜(-x⁴)

Which, this breaks down to.

-∜3740 = x

Now, just do the additional side, which is much easier

∜(x^{4) =} ∜(3740)

 x = ∜3740

In this scenario the ∜ and the x⁴ will cancel out and the ∜ and since the value 3740 is not a rational root is can't go further so, your answer comes out to be.

x = ± ∜3740