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Solve $a = 3 + \sqrt{5a - 9}$ and $b = 1 + \sqrt{5b - 5}$.

 Apr 24, 2022
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The first equation:

 

Subtract 3 from both sides: \(a-3= \sqrt{5a-9}\)

 

Square both terms: \(a^2-6a+9=5a-9\)

 

Bring everything to the left-hand side: \(a^2 -11a+18=0\)

 

Factor: \((a-9)(a-2)=0\)

 

This means \(a = 2\) or \(a = 9\)

 

Plugging these in to check, we find that \(\color{brown}\boxed{a=2}\)

 

Repeat the steps for the 2nd equation, and feel free to ask if you need any help!

 Apr 24, 2022

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