stop@800 wrote:Either work on these type of questions by equation solving or by value substitution.

I preferred second approach in this question

let
x = 1000
y2 = 9
z4 = 1
so
x=1000
y=+-3
z=+-1

take 1000 3 1
and 1000 1 -3
so x>y>z
and x>x>y

Now we need to check the remaining condition also

take
z=1/3
y=1/4
x=1/8

x > y2 > z4 while
z > y > x

So All three are true.
Let me know if you want more detailed explanation about number selection

this is good.

make sure that you get the following TAKEAWAYS from the behavior of the numbers that stop@800 has chosen in this post:

* even powers, such as y^2 and z^4, must be positive.
* if y and z are negative, then their even powers will be ordered in exactly the opposite way than if they were positive.
(illustration: 4 > 2 and 4^2 > 2^2; -2 > -4 but (-2)^2 < (-4)^2.)
* make sure you understand the behavior of FRACTIONS when they are raised to powers; it's the opposite of the behavior of integers of the same sign.
in other words, positive integers (except 1) get larger when they're raised to powers; positive fractions get smaller when they're raised to powers.
negative integers get more negative (i.e., negative, with a bigger absolute value) when they're raised to (odd) powers; negative fractions get less negative (i.e., negative, with a smaller absolute value) when they're raised to those powers.

Indradeep wrote:Another small and easy thing for abstract substitutions like these:
Break up into 3 parts
1. All positive integers
2. Negative integers
3. Numbers from 0->1

If you are going to use substitutions for these questions, don't forget

4. Numbers from -1 to 0.