M7MBA wrote:What is integer x? $$(1)\ \ \ \ x^x=|x|\ $$ $$(2)\ \ \ \ x^2=|x^3|$$ The OA is the option A.
I don't know how to find the correct answer. Experts, could you give me your explanation? Thanks.
(1) x^x = |x|
We cannot consider x = 0 as 0^0 is undefined.
x can be 1 as 1^1 = 1 and |1| = 1.
x cannot be -1 as (-1)^(-1) = 1/(-1) = -1 ≠|1| (= 1).
There is no need to consider other positive integer values as for those values x^x >> |x|. Thus x = 1. Sufficient.
(2) x^2 = |x^3|
x can be any integer among 0, 1 and - 1.
At x = 0, we have x^2 = |x^3| => 0^2 = |0^3| => 0 = 0.
At x = 1, we have x^2 = |x^3| => 1^2 = |1^3| => 1 = 1.
At x = -1, we have x^2 = |x^3| => (-1)^2 = |(-1)^3| => 1 = 1.
No unique value. Insufficient.
The correct answer:
A
Hope this helps!
-Jay
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