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

Algebra ->  Equations -> SOLUTION: Solve the equation sqrt(8x) + sqrt(2x)- sqrt(x/8) =110.       Log On


   

Question 987319: Solve the equation sqrt(8x) + sqrt(2x)- sqrt(x/8) =110. 
Answer by ikleyn(52784) 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.