Problem Solving (PS) | Re: If x is an even integer and x^2 + 6 > 22, which of the following inequ

x : even integer
x^2 + 6 > 22
Find: must be true condition

Here we know x is even but we don't know if x is -ve or +ve
x^2 + 6 > 22 => x^2>16 so implies x<-4 or x>4

Now going through options

A. x^4 > 231
x^2 > 16
=> x^4 > 16^2 => x^4>256 => x^4>256 > 231
Always true condition: for both x -ve or x +ve
Answer

B. x^3 > 64
we know x^2 >16 => x =+ve or x=-ve
what if x =-ve so x^3 will be -ve so x^3 > 64 will not be true if x =-ve

C.
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