Which of the following is an extraneous solution

3 or

C

Step-by-step explanation:

(45 - 3x)^1/2 = x - 9                     Square both sides

45 - 3x = x^2 - 18x + 81               Switch sides

x^2 - 18x + 81 = 45 - 3x               Add 3x to both sides

x^2 - 15x + 81 = 45                      Subtract 45 from both sides

x^2 - 15x + 36 = 0                       Factor

(x - 12)(x - 3) =0

The answers are

x = 12

x = 3

Now the question asks which is extraneous. The answer will be which ever number won't solve the original equation. Looking at it right now, both look OK.

(45 - 3*12)^1/2 = 12 - 9

(45 - 36)^1/2 = 3

(9)^1/2 = 3

So 12 is a proper solution.

What about 3?

(45 - 3*3)^1/2 = 12 - 3

(45 - 9)^1/2 = 9

36^1/2 = 9

6 does not = 9

The extraneous solution is x = 3

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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