the sum of a non-negative number and its square is lessthan 12. What could the number be?
Answer
answer
Answer
http://www.jiskha.com/display.cgi?id=1452170576
IBM
Hmm, let me think about this for a moment... Ah, I've got it! The number could be anything that's greater than 0 and less than 3. Just like trying to catch a butterfly, stay between 0 and 3 to make sure the sum of the number and its square is less than 12. Good luck, butterfly catcher! 🦋
To solve this problem, we can set up an equation based on the information given. Let's assume the number we're looking for is represented by "x".
Given that the sum of a non-negative number and its square is less than 12, we can write the equation as follows:
x + x^2 < 12
Next, we need to solve this inequality to determine the possible values of x.
To do this, we can rearrange the equation and set it equal to 0:
x^2 + x - 12 < 0
Now, we can factorize the quadratic equation:
(x - 3)(x + 4) < 0
To satisfy the condition of a negative result, we need to determine the ranges of x that make the expression less than zero.
Using the concept of intervals, we have three critical points: -4, 0, and 3.
We can test values from each interval to see which interval satisfies the inequality.
For x < -4:
Choose x = -5:
(-5 - 3)(-5 + 4) = (-8)(-1) > 0 (not less than 0)
For -4 < x < 0:
Choose x = -2:
(-2 - 3)(-2 + 4) = (-5)(2) < 0 (satisfies the inequality)
For 0 < x < 3:
Choose x = 1:
(1 - 3)(1 + 4) = (-2)(5) > 0 (not less than 0)
For x > 3:
Choose x = 4:
(4 - 3)(4 + 4) = (1)(8) > 0 (not less than 0)
Therefore, we find that -4 < x < 0 is the range for which the expression is less than 0. So, the possible values for the non-negative number x in this case are between -4 and 0 (exclusive).