Question

Find the solutions to 0 ≥ x4 – 1

Answer 1

is this ur question?
\[0 \ge x^4-1.\]???????????????????????????????????????????????????????????????????????????

Answer 2

@chase3 ????????????????????????????????

Answer 3

yes

Answer 4

so am i suppose to start my x values with -1, 0, 1 ,2

Answer 5

so im only going to have two x values

Answer 6

no a set of values

Answer 7

i think u need more clarification.

Answer 8

yea that is what im talking about ... explain to me how i would put that on a function chart

Answer 9

wait a minute i m going wrong

Answer 10

We would have 4 values

-1, +1, -i, +i .

Ok!

Answer 11

ok

Answer 12

I think this question is going on high level than mine!
I don't know wt to do of imaginary critical points
that is - i & +i.

So i think @waterineyes Plz help:D

Answer 13

We have done only this much
\[x^4-1 \le 0.\]\[\implies (x^2+1)(x^2-1) \le 0.\]\[\implies (x^2+1)(x+1)(x-1) \le 0.\]So critical point are : -\[+1, -1, +i , -i.\]
But wt to do now????????????

Answer 14

i think your'e just suppose to plug in the x values into the equation

Answer 15

i think strictly NO

Answer 16

we want a representation of this inequality to get the correct solution set.

Answer 17

but how to represent it?

Answer 18

@Ishaan94 @amistre64 @mathslover @phi Plz help:)

Answer 19

@waterineyes too plz :)

Answer 20

i really do think we're over thinking the question

Answer 21

\[\large{0\ge x^4-1}\]
\[\large{0+1 \ge x^4-1+1}\]
\[\large{1 \ge x^4}\]
\[\large{1\ge (x)^4}\]
\[\large{\sqrt[4]{1}\ge x}\]
\[\large{1\ge x}\]

Answer 22

thanks for tagging me here @maheshmeghwal9

Answer 23

but im pretty sure the answer is suppose to be in a table chart

Answer 24

If you are allowing complex values, the solution is the complex numbers less than or equal to the unit circle.

Answer 25

either x = 1 or x<1

Answer 26

If you are only dealing with real numbers
then -1≤ x ≤ 1

Answer 27

so @phi you think that is the answer

Answer 28

try it. (-1)^4 - 1 = 0 which agrees with ≤ 0
clearly fractions less than 1 raised to the 4th power are < 1, and we match the condition

Answer 29

if you allow complex numbers then
x= A exp(i theta) where |A|≤ 1, 0≤theta≤ 2pi
will meet the condition.

Answer 30

alright will do