smartguy595 wrote:
Can Someone explain how the below are deduced.
X^8>1-->X<-1 OR X>1
X^8<1--->-1<X<1
Hi,
when you raise anything less than 1 to an integer power, it becomes smaller as the power increases..
example 1/2.. 1/2 ^2=1/4.. 1/2^3=1/8...
lets see the two inequalities now..
X^8>1..
since the power of x is even number 8, x^8 will always be positive..
so if x is any negative integer less than -1, x^8 will >1..
example x=-2, (-2)^8 will be greater than 1..
but as we have seen earlier anything less than 1 when raised to a power will become even smaller, so it will always be<1..
that is why x cannot take any value between -1 and 1, both inclusive, for x^8 to be >1..
so x<-1 or x>1..
x^8<1..
Opposite of the above , for x^8 to be less than 1, x has to be between 1 and -1..
hope it helps
yes it is 100% clear.. Thank you so much
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