Multiple choice

Solve the equation $\sqrt{2x-6} +\sqrt{x + 4} = 5$

  1. 2

  2. 4

  3. 5

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Testing option C: sqrt(2*5-6) + sqrt(5+4) = sqrt(4) + sqrt(9) = 2 + 3 = 5. This satisfies the equation.

AI explanation

Isolate one radical to get sqrt(2x - 6) = 5 - sqrt(x + 4). Squaring both sides gives 2x - 6 = 25 - 10 * sqrt(x + 4) + x + 4, which simplifies to x - 35 = -10 * sqrt(x + 4). Squaring again yields x^2 - 70x + 1225 = 100(x + 4), or x^2 - 170x + 825 = 0. Factoring this gives (x - 5)(x - 165) = 0; checking both solutions, x = 5 works in the original equation while x = 165 is extraneous.

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