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inequalities with an exponent

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inequalities with an exponent

by Taniuca » Wed Oct 05, 2011 5:44 pm
Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.

Is (y+3)^2 less than 4?
(1) y+3 is less than 2.

(2) y+3 is greater than .

They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
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by Anurag@Gurome » Wed Oct 05, 2011 7:50 pm
Taniuca wrote:Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.

Is (y+3)^2 less than 4?

(1) y+3 is less than 2.
(2) y+3 is greater than .

They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
Is (y + 3)² less than 4?

We can take examples to be more clear.

(1) (y + 3) < 2
If y = -2, then (y + 3)² = (-2 + 3)² = 1 < 4
If y = -6, then (y + 3)² = (-6 + 3)² = 9 > 4
No definite answer; NOT sufficient.

(2) I guess it is (y + 3) > -2
If If y = -2, then (y + 3)² = (-2 + 3)² = 1 < 4
If y = 4, then (y + 3)² = (4 + 3)² = 49 > 4
No definite answer; NOT sufficient.

Combining (1) and (2), we know that -2 < (y + 3) < 2. So, (y + 3)² < 4; SUFFICIENT.

The correct answer is C.
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by sl750 » Thu Oct 06, 2011 2:21 am
Taniuca wrote:Hello, I need some help! I found this problem and I do not know what rule it was applied when solving the problem.

Is (y+3)^2 less than 4?
(1) y+3 is less than 2.

(2) y+3 is greater than .

They say, "The Inequality (y+3)^2 < 4 is equivalent to -2 < y+3 < 2. Will this be truth for any given exponent to have a two side inequality to the power? what if the power is negative? what direction should it be?
Your help will be appreciatted! correct Answer is C
If the exponent,as in this case is 2, you have two real roots, one positive and one negative. Also, in this case, the inequality used is less than, hence the expression, y+3 is in between the range +/-2. Had it been the other way around, where (y+3)^2>4, the result would be (y+3>2 or (y+3)<-2.
For higher order exponents, like say, n=4, you have 2 real roots and 2 complex roots
For n=3, you have one real root and 2 complex roots. Also for odd exponents it is possible to have negative real roots. Ex cuberoot(-8) = -2

The inequality sign changes when you multiply both sides by a negative quantity or divide by a nonzero negative number
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