word problem

Question

the square root of three times a number is six less than the number

Answer 1

Hello G,

 

Set up an equation:

 

√(3x) = x-6

(√(3x))² = (x-6)²

3x = (x-6)(x-6)

3x = x² - 12x + 36

0 = x² - 15x + 36

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

 

x = 3, x = 12

 

It is important to check for extraneous roots....

 

If we put 3 in for x:

 

√9 ≠ 3-6

3 ≠ -3

 

AAIINNTTTT... thanks for playing.... NO, this doesn't work.

 

If we put 12 in for x:

 

√36 = 12 -6

6 = 6

 

DING! DING! DING! YES! We have a winner!!!

 

The only solution is x = 12.

 

I hope this helps.

Answer 2

√(3x) = x-6

square both sides

3x = x² - 12x + 36

 

set to zero

 

0 = x² -15x + 36

 

factor

 

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

 

so x = 3 or 12, but the original phrasing of the problem defines the problem in the terms of the square root function which usually implies that the primary square root, the one greater than zero, is being sought,

 

so it would be proper to answer 12, not 3 and 12.