What is the answer to 1/(sqrt(x))= 2/x ?

The answer to 1/(sqrt(x))= 2/x is x=4

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1/(sqrt(x))= 2/x

\frac{1}{x} = \frac{2}{x}

x = 4

Solution steps

\frac{1}{x} = \frac{2}{x}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot x = x \cdot 2

Expand

1 \cdot x : x

x = x \cdot 2

Square both sides:

x^{2} = 4 x

x^{2} = 4 x

Solve

x^{2} = 4 x : x = 4, x = 0

x = 4, x = 0

Verify Solutions:

x = 4

True

, x = 0

False

The solution is

x = 4

6 - x + 2 = x - 2

13 = - 4 x - 8 + 3

4 x = 16 x^{2} + 6 x - 12

2 x - 1 - 2 x - 4 = 3

x - 1 = 10