x^4 - x <0?

Question

How do you solv this?
At first i trying moving the zero over but it didnt work..

how is x less than 1?

i still cant understand how you get that.. can someone show me the steps

Answer 1

x^4 - x < 0
x(x^3 - 1) < 0
x(x - 1)(x^2 + x + 1) < 0

Now x^2 + x + 1 > 0 for every x.

f(x) = x is less than zero from every x < 0 and is positive for x > 0.

g(x) = x - 1 is negative for x < 1 and positive for x > 1.

So the product f(x)*g(x) is negative for 0 < x < 1

Answer 2

Add x to both sides of the equation to give you x^4 < x. After that, divide both sides by x. Here's where it gets tricky: when using equalities, dividing or multiplying by a negative number will switch the direction of the inequality, and since you haven't yet found x, you don't know if it's negative or positive. So you might be tempted to create two equations: x^3 < 1 if x is positive, or x^3 > 1 if x is negative because you just divided by a negative number. (In case you're lost, x^4 / x = x^3 and x / x = 1.)
However, the original problem gives you a clue as to which is the proper equation. The left side of the inequality shows x^4. The laws of powers state that if any number, positive or negative, is raised to an even numbered power, then the result MUST be positive. Therefore x^4 is positive. Since x is greater than x^4, x must also be positive. Therefore the proper answer (so far) is x^3 < 1. We can then take the cube root of both sides and find that x < 1. Because we have already proved that x is positive, we can define the final inequality as:

0 < x < 1

Answer 3

look
x^4-x<0 <=> x(x^3-1)<0 <=> x(x-1)(x^2+x+1)<0 .
Now the parts mustnt have the same + or -.but the third part is always positive . so you check when the two firsts are negative (as one of course) and in this space x belongs

Answer 4

try it for 0 < x < 1

Answer 5

x^4 - x < 0
x(x^3 - 1) < 0
x(x - 1)(x^2 + x + 1) < 0

using only the real solutions

0 < x < 1

the reason for the answer is because

-1(-1 - 1) = -1(-1 + (-1)) = -1(-2) = 2, which is above 0 not below
2(2 - 1) = 2(1) = 2, which is above 0 not below

Answer 6

x is less than 1