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

Apr 24, 2022

#1
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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