Question

Solve the non-linear inequality. Express the solution in interval notation. x^4 is greater than x^2

Answer 1

\[x^4>x^2\]

Answer 2

I take the square root of both sides and get the plus or minus square root of x^2 is greater than x, then I take the square root of x^2 and x to get x is greater than the plus or minus square root of x

Answer 3

\[x ^{4}>x ^{2}\]

\[x ^{4}-x ^{2}>0\]

\[x ^{2}(x ^{2}-1)>0\]

\[x ^{2}>0 or x ^{2}>1\]

x>0 or x<-1 or x>1 then x<-1 and x>0 will be the interval...

Answer 4

\(x^2(x^2-1)>0\) divide it by \(x^2\):
\((x-1)(x+1)>0\)
\(x\in(-\infty;-1)\bigcup(1;\infty)\)

Answer 5

why is it greater than 0

Answer 6

oh subtract the x^2?

Answer 7

yep//....

Answer 8

@znimon understood the process?

Answer 9

almost, what about after x^2(x^2-1) is greater than 0

Answer 10

\(x^2\) is always bigger than 0. It equals 0 when \(x=0\). But it doesn't satisfy the inequality.

Answer 11

took x^2 common in both the terms....

Answer 12

yep got that

Answer 13

nops.. while splitting the inequality x has to be >0

Answer 14

will you break it down after the x^2(x^2-1) is greater than 0

Answer 15

yep.... both the split terms are compared to the inequalities...

Answer 16

I understand how it works so I need to find all the solutions for x that satisfy the inequality

Answer 17

thanks now I'll try some on my own. Will you recommend a problem that has the same properties?

Answer 18

@sriramkumar

Answer 19

try this one... \[x ^{8}-x ^{2}<0\] remeber x^3 has different properties when compared with x^2 .... have a good time!!!!1

Answer 20

thanks

Answer 21

@znimon you're welcome :)))))))))))))))))

Answer 22

\[\ \ x^4\ge x^2\\ \ \ x^2[x^2]\ge x^2\\x^2\text{ is either 0 non-zero.}\\
\text{if }x^2\text{ is 0,}\\
\ \ 0\times0=0\\
\ \ 0 = 0\\
\text{therefore }x^2[x^2]\ge x^2\\
\text{otherwise,}\\
\ \ x^2\ge1\\
\ \ |x|\ge\sqrt1\]

Answer 23

is either 0 or non-zero **

Answer 24

solution is \[x <0, x <1] so (negative infinity, to 0 not including zero)?

Answer 25

for x^3-x^2 is less than 0