Answer:
Some k's that will work:
1/2
1/3
1/4
(There are infinitely many answers.)
Step-by-step explanation:
Obviously 5 won't work because 25<5 is not true.
What about a negative? -5?
25<-5 is not true.
How about 1/3? 1/9<1/3 is true so 1/3 works.
Note: Think of a number between 0 and 1.
1/4<1/2 is true and (1/2)^2=1/4.
1/16<1/4 is true and (1/4)^2=1/16.
You can solve k^2<k.
Subtract k on both sides.
k^2-k<0
Factor.
k(k-1)<0.
So k^2-k is a parabola with x-intercepts (k-intercepts) at k=0 and k=1.
The parabola is open up so any number between 0 and 1 will satisfy k^2<k since between 0 and 1 the parabola is less than y=0 ( the x-axis).
