How do you solve #|x-2| =|x^2-4|#?
Given:
We must have one of the following:
So all the possible solutions are solutions of the original equation.
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To solve the equation |x-2| = |x^2-4|, you need to consider two cases:
- When ( x - 2 ) is positive or zero, ( |x-2| = x - 2 ).
- When ( x - 2 ) is negative, ( |x-2| = -(x - 2) = 2 - x ).
For case 1: ( |x-2| = x - 2 ) ( |x^2-4| = x^2 - 4 )
For case 2: ( |x-2| = 2 - x ) ( |x^2-4| = -(x^2 - 4) = 4 - x^2 )
Solve each case separately and then check if the solutions satisfy the original equation.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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