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For alt=0 , determine all real roots of ...

For `alt=0` , determine all real roots of the equation (1986, 5M) `x^2-2a|x-a|-3a^2=0`

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To solve the equation \( x^2 - 2a|x - a| - 3a^2 = 0 \) for \( a \leq 0 \), we will consider two cases based on the definition of the absolute value. ### Step 1: Case 1 - \( x \geq a \) In this case, \( |x - a| = x - a \). Therefore, we can rewrite the equation as: \[ x^2 - 2a(x - a) - 3a^2 = 0 \] Expanding this gives: ...
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