What is the answer to 3sqrt(x)+3x^{-1/2}=10 ?

The answer to 3sqrt(x)+3x^{-1/2}=10 is x=9,x= 1/9

3sqrt(x)+3x^{-1/2}=10

3 x + 3 x^{- \frac{1}{2}} = 10

x = 9, x = \frac{1}{9}

Decimal

x = 9, x = 0.11111 \dots

Solution steps

3 x + 3 x^{- \frac{1}{2}} = 10

Expand

3 x + 3 x^{- \frac{1}{2}} : 3 x + \frac{3}{x ^{\frac{1}{2}}}

3 x + \frac{3}{x ^{\frac{1}{2}}} = 10

Remove square roots

81 x^{2} - 1800 x + \frac{81}{x ^{2}} + \frac{1800}{x} + 9838 = \frac{3600}{x}

Solve

81 x^{2} - 1800 x + \frac{81}{x ^{2}} + \frac{1800}{x} + 9838 = \frac{3600}{x} : x = 9, x = \frac{1}{9}, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

x = 9, x = \frac{1}{9}, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

Verify Solutions:

x = 9

True

, x = \frac{1}{9}

True

, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

False

, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

False

The solutions are

x = 9, x = \frac{1}{9}

x - x - 5 = 0

\frac{2}{x} - 1 = 0

3 2 x + 2 + 6 = 8

x + 1 - 2 x - 4 = 0

x + 1 = 5 - 3

What is the answer to 3sqrt(x)+3x^{-1/2}=10 ?
The answer to 3sqrt(x)+3x^{-1/2}=10 is x=9,x= 1/9
Solve for x: 3sqrt(x)+3x^{-1/2}=10
The solution is x=9,x= 1/9