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15 votes
15 votes
What is the solution set of the equation?

√(x) -18+9x=x

User Ecropolis
by
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1 Answer

14 votes
14 votes

9514 1404 393

Answer:

x ∈ {2.07014981016}

Explanation:

The equation can be rewritten as ...

√x = 18-8x

x = 324 -288x +64x²

64x² -289x +324 = 0

x = (289 ±√577)/128 ≈ {2.07015, 2.44548}

Since √x must be positive, we know that ...

18 -8x ≥ 0

x ≤ 18/8 = 2.25

The larger of the above solutions is extraneous, so the solution set is ...

x ∈ {(289 -√577)/128} ≈ {2.07015}

User Keeely
by
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