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

The answer to ((x+1/x)^{1/2}+(x+1/x)1)/2 =x is x\approx 2.08101…

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((x+1/x)^{1/2}+(x+1/x)1)/2 =x

\frac{( x + \frac{1}{x} ) ^{\frac{1}{2}} + ( x + \frac{1}{x} ) 1}{2} = x

x \approx 2.08101 \dots

Solution steps

\frac{( x + \frac{1}{x} ) ^{\frac{1}{2}} + ( x + \frac{1}{x} ) \cdot 1}{2} = x

Multiply both sides by

2

\frac{( x + \frac{1}{x} ) ^{\frac{1}{2}} + ( x + \frac{1}{x} ) \cdot 1}{2} \cdot 2 = x \cdot 2

Simplify

(x + \frac{1}{x})^{\frac{1}{2}} + x + \frac{1}{x} = x \cdot 2

Remove square roots

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

Solve

x + \frac{1}{x} = x^{2} - 2 + \frac{1}{x ^{2}} : x \approx 0.48053 \dots, x \approx 2.08101 \dots

x \approx 0.48053 \dots, x \approx 2.08101 \dots

Verify Solutions:

x \approx 0.48053 \dots

False

, x \approx 2.08101 \dots

True

The solution is

x \approx 2.08101 \dots

(7 x)^{\frac{1}{3}} = x^{\frac{1}{2}}

x = 5 x - 4

8 = 3 + (m - 9)^{\frac{1}{2}}

x + 2 = x

2 x - 3 = 4

What is the answer to ((x+1/x)^{1/2}+(x+1/x)1)/2 =x ?
The answer to ((x+1/x)^{1/2}+(x+1/x)1)/2 =x is x\approx 2.08101…
Solve for x: ((x+1/x)^{1/2}+(x+1/x)1)/2 =x
The solution is x\approx 2.08101…