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MC-III Algebra 5.24

 
 
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MC-III Algebra 5.24
by Wen Shen - Wednesday, 15 April 2020, 3:27 PM
 

I started by squaring both sides. What I ended up getting was 3x-4+a-2(sqrt(2x^2-4x+2ax-4a)) = 1. I don't know how to continue from here. I know that I haven't used the fact that the value of a will only leave 1 root, but I don't know how to use it. 

 
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Re: MC-III Algebra 5.24
by Areteem Professor - Wednesday, 15 April 2020, 5:29 PM
 

You squared both sides once to at least start getting rid of the square roots, so isolating the square root and squaring again might be helpful. Note this will still result in a quadratic equation when done correctly.

Then we want the resulting quadratic to have one integer root. What do we know about the discriminant when a quadratic equation has integer/rational roots?

Final caution/hint: squaring might introduce extraneous roots.

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Re: MC-III Algebra 5.24
by Wen Shen - Thursday, 16 April 2020, 9:37 AM
 

Thank you!