What is the answer to 2sqrt(x)+2x^{(-1)/2}=5 ?

The answer to 2sqrt(x)+2x^{(-1)/2}=5 is x=4,x= 1/4

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2sqrt(x)+2x^{(-1)/2}=5

2 x + 2 x^{\frac{- 1}{2}} = 5

x = 4, x = \frac{1}{4}

Decimal

x = 4, x = 0.25

Solution steps

2 x + 2 x^{\frac{- 1}{2}} = 5

Expand

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

2 x + \frac{2}{x ^{\frac{1}{2}}} = 5

Remove square roots

16 x^{2} - 200 x + \frac{16}{x ^{2}} + \frac{200}{x} + 593 = \frac{400}{x}

Solve

16 x^{2} - 200 x + \frac{16}{x ^{2}} + \frac{200}{x} + 593 = \frac{400}{x} : x = 4, x = \frac{1}{4}, x = \frac{33 + 5 \cdot 4 1 ^{\frac{1}{2}}}{8}, x = \frac{33 - 5 \cdot 4 1 ^{\frac{1}{2}}}{8}

x = 4, x = \frac{1}{4}, x = \frac{33 + 5 \cdot 4 1 ^{\frac{1}{2}}}{8}, x = \frac{33 - 5 \cdot 4 1 ^{\frac{1}{2}}}{8}

Verify Solutions:

x = 4

True

, x = \frac{1}{4}

True

, x = \frac{33 + 5 \cdot 4 1 ^{\frac{1}{2}}}{8}

False

, x = \frac{33 - 5 \cdot 4 1 ^{\frac{1}{2}}}{8}

False

The solutions are

x = 4, x = \frac{1}{4}

(1) 9 x^{2} - 25 = 12

3 x - 5 + 3 x - 14 = 9

a, 11 + 21 = \frac{a}{b} + \frac{c}{d}

x^{\frac{1}{2}} = 9

x - 1 = 3 - x

What is the answer to 2sqrt(x)+2x^{(-1)/2}=5 ?
The answer to 2sqrt(x)+2x^{(-1)/2}=5 is x=4,x= 1/4
Solve for x: 2sqrt(x)+2x^{(-1)/2}=5
The solution is x=4,x= 1/4