If #4-x^2>=0# isn't #x<=+-2#? I don't understand how #-2<=x<=2# is a result.

Question

#4-x^2>=0# isn't #x<=+-2#?
I don't understand how #-2 <=x<=2# is the result?

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Answer 1 · 2017-12-28T08:38:13

Please see below.

As #4-x^2>=0#, we have #(2-x)(2+x)>=0#

This means product of #(2-x)# and #(2+x)# is positive. Hence either both are positive or both are negative.

If both are positive we have #2-x>=0# i.e. #x<=2# and #2+x>=0# i.e. #x>=-2#. Hence we have #-2<=x<=2#.

If both are negative we have #2-x<=0# i.e. #x>=2# and #2+x<=0# i.e. #x<=-2#. We cannot have the two together.

Hence answer is #-2<=x<=2#