Question 637713
solve this equation in step by step ?
{{{sqrt(2/x) - sqrt (x/2)}}} = {{{1/sqrt(2)}}}
Square both sides
{{{(sqrt(2/x) - sqrt(x/2))^2}}} = {{{1/2}}}
:
FOIL
{{{(sqrt(2/x)-sqrt (x/2))}}})*({{{sqrt(2/x)-sqrt(x/2))}}}
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Results
{{{2/x}}} - {{{sqrt((2x)/(2x))}}} - {{{sqrt((2x)/(2x))}}} + {{{x/2}}} = {{{1/2}}}
:
2x/2x = 1, square root of 1 is 1 therefore
{{{2/x}}} - 1 - 1 + {{{x/2}}} = {{{1/2}}}
:
{{{2/x}}} - 2 + {{{x/2}}} = {{{1/2}}}
:
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