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

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

the correct answer is the second option