SOLUTION: Solve the equation and sqrt( 8x ) + sqrt( 2x )- sqrt( x/8 ) =110. 

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Question 987318: Solve the equation and sqrt( 8x ) + sqrt( 2x )- sqrt( x/8 ) =110. 
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your equation is

sqrt%288x%29 + sqrt%282x%29- sqrt%28x%2F8%29 = 110. 

Notice that

sqrt%288x%29 = sqrt%288%29sqrt%28x%29 = 2sqrt%282%29sqrt%28x%29,

sqrt%282x%29 = sqrt%282%29sqrt%28x%29,     and

sqrt%28x%2F8%29 = sqrt%281%2F8%29sqrt%28x%29 = 1%2F%282sqrt%282%29%29sqrt%28x%29 = sqrt%282%29%2F%282%2A2%29sqrt%28x%29 = sqrt%282%29%2F4sqrt%28x%29.

Hence,  your equations takes the form

2sqrt%282%29sqrt%28x%29 + sqrt%282%29sqrt%28x%29 - sqrt%282%29%2F4sqrt%28x%29 = 110,     or

%282sqrt%282%29+%2B+sqrt%282%29+-+sqrt%282%29%2F4%29sqrt%28x%29 = 110,

Now,  multiply both sides by  4  and then collect the common terms:

%288sqrt%282%29+%2B+4sqrt%282%29+-+sqrt%282%29%29sqrt%28x%29 = 440,

11sqrt%282%29sqrt%28x%29 = 440.

Hence,

sqrt%28x%29 = 440%2F%2811sqrt%282%29%29 = 40%2Fsqrt%282%29 = %2840%2Asqrt%282%29%29%2F2 = 20sqrt%282%29.

Therefore,  x = 400*2 = 800.

Answer.  x = 800.


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the equation and sqrt( 8x ) + sqrt( 2x )- sqrt( x/8 ) =110. 
sqrt%288x%29+%2B+sqrt%282x%29+-+sqrt%28x%2F8%29+=+110

sqrt%288x%29+%2B+sqrt%282x%29+-+sqrt%28x%29%2Fsqrt%288%29+=+110

 ------- Multiplying by LCD, sqrt%288%29

sqrt%2864x%29+%2B+sqrt%2816x%29+-+sqrt%28x%29+=+110sqrt%288%29

8sqrt%28x%29+%2B+4sqrt%28x%29+-+sqrt%28x%29+=+110sqrt%288%29

11sqrt%28x%29+=+110sqrt%288%29

sqrt%28x%29+=+10sqrt%288%29 --------- Dividing both sides by 11

x+=+100+%2A+8 --------- Squaring both sides

highlight_green%28x+=+800+%29