SOLUTION: What is the best way to solve this equation in step by step ? {{{sqrt(2/x) - sqrt (x/2) = 1/sqrt (2) }}} I'm profoundly grateful for help.

Algebra ->  Radicals -> SOLUTION: What is the best way to solve this equation in step by step ? {{{sqrt(2/x) - sqrt (x/2) = 1/sqrt (2) }}} I'm profoundly grateful for help.       Log On


   

Question 637713: What is the best way to solve this equation in step by step ?
sqrt%282%2Fx%29+-+sqrt+%28x%2F2%29+=+1%2Fsqrt+%282%29+
I'm profoundly grateful for help.
Found 2 solutions by MathTherapy, ankor@dixie-net.com:
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the best way to solve this equation in step by step ?
sqrt%282%2Fx%29+-+sqrt+%28x%2F2%29+=+1%2Fsqrt+%282%29+
I'm profoundly grateful for help.

sqrt%282%2Fx%29+-+sqrt+%28x%2F2%29+=+1%2Fsqrt+%282%29+

sqrt%282%29%2Fsqrt%28x%29+-+sqrt%28x%29%2Fsqrt%282%29+=+1%2Fsqrt+%282%29+ ---- Separate the radicals

%28sqrt%282%29%2Asqrt%282%29%29+-+%28sqrt%28x%29%2Asqrt%28x%29%29+=+sqrt%28x%29 ----- Multiplying equation by LCD, sqrt%28x%29%2Asqrt%282%29

sqrt%282%5E2%29+-+sqrt%28x%5E2%29+=+sqrt%28x%29

2+-+x+=+sqrt%28x%29

%282+-+x%29%5E2+=+%28sqrt%28x%29%29%5E2 ----- Squaring both sides of equation

4+-+4x+%2B+x%5E2+=+x

x%5E2+-+4x+-+x+%2B+4+=+0

x%5E2+-+5x+%2B+4+=+0

(x - 4)(x - 1) = 0

x = 4 or x = 1

Substituting 4 for x in original equation results in x = 4 being an EXTRANEOUS solution. On the other hand, substituting 1 for x makes the original equation true, so highlight_green%28x=1%29.

You can do the checks by plugging in 4 for x, and then 1 for x in original equation.

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve this equation in step by step ?
sqrt%282%2Fx%29+-+sqrt+%28x%2F2%29 = 1%2Fsqrt%282%29
Square both sides
%28sqrt%282%2Fx%29+-+sqrt%28x%2F2%29%29%5E2 = 1%2F2
:
FOIL
%28sqrt%282%2Fx%29-sqrt+%28x%2F2%29%29)*(sqrt%282%2Fx%29-sqrt%28x%2F2%29%29
:
Results
2%2Fx - sqrt%28%282x%29%2F%282x%29%29 - sqrt%28%282x%29%2F%282x%29%29 + x%2F2 = 1%2F2
:
2x/2x = 1, square root of 1 is 1 therefore
2%2Fx - 1 - 1 + x%2F2 = 1%2F2
:
2%2Fx - 2 + x%2F2 = 1%2F2
:
Multiply each term by 2x, to clear the denominators, results
2(2) - 4x + x^2 = x
Combine on the left to form a quadratic equation
x^2 - 5x - x + 4 = 0
x^2 - 5x + 4 = 0
Factors to:
(x-4)(x-1) = 0
two solutions
x=4
x=1