SOLUTION: Find all numbers whose squares are less than the numbers.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Find all numbers whose squares are less than the numbers.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 659859: Find all numbers whose squares are less than the numbers.
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Because the square of a negative number is a positive number, we know x >= 0.
We are looking for all x such that x%5E2+%3C+x
Dividing both sides by x (with the requirement that x<>0) gives
%28x%5E2%29%2Fx+%3C+x%2Fx, x%3C%3E0
x+%3C+1, x%3C%3E0
So we have narrowed it down to 0 <= x < 1.
And since 0%5E2+=+0, we can eliminate 0.
So we can say x%5E2+%3C+x for all 0 < x < 1.