vipulgoyal wrote:Mitch please explain
here in solution why inequality changed, i believe its not multiplied by - both sides
x-1 < -2
x < -1
(x-1)² > 4.
When we solve with regard to the NEGATIVE square root of 4, the following is implied:
(x-1)² > (-2)²
Here, when we take the square root of each side, we are in effect DIVIDING each side by a negative value, so the direction of the inequality must change:
(x-1)² > (-2)²
(x-1)(x-1) > (-2)(-2)
(x-1)(x-1) /
(x-1) < (-2)(-2) /
(-2) Each side is divided by a negative value, so > changes to <.
x-1 < -2
x < -1.
In general, when an inequality includes a square root, flip the inequality when solving for the negative root:
If (x-1)² > 4, then either x-1 > 2 or x-1 < -2.
If (x+2)² < 9, then either x+2 < 3 or x+2 > -3.
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