Math CentralQuandaries & Queries


Question from Crystal, a student:

I need to solve this radical equation but i am confused on how to solve it with three square roots in it.


I would rewrite this as

√(3x) + 3 = √(3x-2) + √(2x-3)

and then square both sides. This will yield an equation with 6√(3x) on the left, 2√[(3x-2) (2x-3)] on the right and a few other terms. Rewrite this equation with 6√(3x) - 2√[(3x-2) (2x-3)] on the left and all the remaining terms on the right. Square both sides again to produce an equation with only one square root term. Rearrange and square again to finally yield an equation with no roots. Solve this equation for x. Make sure you verify any potential solutions you find as all the squaring might introduce extraneous solutions.


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