SOLUTION: Find the product of all values of x that make the following equation true.{{{ ( sqrt( 2x ) + sqrt( 2/x ) - 2 * sqrt( 2 )) / ( sqrt( 2x )+ sqrt( 2/x )) = ( sqrt( 2x ) + sqrt( 2/x ))

Question 1104240: Find the product of all values of x that make the following equation true. , x doesn't equal 0.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Since the problem specifies that x is not 0, we can simplify the form of the equation greatly by multiplying every term in the numerator and denominator of both fractions by . That will make the equation

Solving by "cross multiplying"...

Since the problem asked for the product of the roots -- and not for the actual roots -- we can at this point say the product is 4/4 = 1, using the fact that the product of the roots of the quadratic equation ax^2+bx+c=0 is c/a.

So the answer to the problem is: the product of the roots of the equation is 1.

However, the quadratic expression factors nicely, making it easy to find the actual roots:

The roots are x=1/4 and x=4.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

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