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Find all values of x such that \sqrt{4x^2} + \sqrt{x^2} = 6 + 3x.

 Jun 28, 2023
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Find all values of x such that \sqrt{4x^2} + \sqrt{x^2} = 6 + 3x.   

 

I thought I had this figured out in an earlier posting of this same question,   

but a moderator, Alan, added an answer, as a correction of the mistake   

that I had made in my answer.  Here's a copy/paste of what Alan said:   

 

Note there is a difference between  x^2 = 4, for which x = ±2,  and  x = √4, for which x = +2 only.   

 

√(4x^2) = 2∣x∣    and    √(x^2) = ∣x∣   

 

so we have:   3∣x∣ = 6 + 3x    

.

 Jun 28, 2023

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