Answers

  • Brainly User
2016-01-07T15:50:57+08:00
 \frac{ \sqrt{6x-2} }{x-2} =2

( \frac{ \sqrt{6x-2}}{x-2} ) ^{2}  = (2) ^{2}

 \frac{6x-2}{x ^{2} -4x+4} =4

6x - 2 = 4(x² - 4x + 4)

6x - 2 = 4x² -16x + 16

4x² - 16x - 6x + 16 + 2 = 0

4x² - 22x + 18 = 0

2 (2x² - 11x + 9) = 0

Factor 2x² - 11x + 9

(2x - 9) (x + 1) = 0

2x - 9 = 0
2x = 9
2x/2 = 9/2
x = 9/2

x - 1 = 0
x = 1

The number is 9/2 or 1.

Check:
x = 9/2
 \frac{ \sqrt{6(9/2)-2} }{(9/2)-2} =2

 \frac{ \sqrt{27-2} }{9/2)-(4/2)} =2

 \frac{ \sqrt{25} }{(5/2)} =2

 \frac{5}{(5/2)} =2

(5) (2/5) = 2

2 = 2  (true)

x = 1
 \frac{ \frac{+}{-}  \sqrt{(6)(1)-2} }{1-2} =2

 \frac{ \frac{+}{-} \sqrt{4}  }{-1} =2

Choose the negative root

 \frac{-2}{-1} =2

2 = 2 (true)



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thank you momgie, your a life saver... =)