What is the answer to (sqrt(x))/x+1+sqrt(x)+1/x = 17/4 ?

The answer to (sqrt(x))/x+1+sqrt(x)+1/x = 17/4 is x=0.80739…,x=7.59196…

Solve for x: (sqrt(x))/x+1+sqrt(x)+1/x = 17/4

The solution is x=0.80739…,x=7.59196…

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\frac{x}{x} + 1 + x + \frac{1}{x} = \frac{17}{4}

x = 0.80739 \dots, x = 7.59196 \dots

Solution steps

\frac{x}{x} + 1 + x + \frac{1}{x} = \frac{17}{4}

Rewrite the equation with

x = u

\frac{u}{u ^{2}} + 1 + u + \frac{1}{u ^{2}} = \frac{17}{4}

Solve

\frac{u}{u ^{2}} + 1 + u + \frac{1}{u ^{2}} = \frac{17}{4} : u \approx - 0.40390 \dots, u \approx 0.89855 \dots, u \approx 2.75535 \dots

u \approx - 0.40390 \dots, u \approx 0.89855 \dots, u \approx 2.75535 \dots

Substitute back

u = x,

solve for

x

Solve

x = - 0.40390 \dots :

No Solution for

x \in R

Solve

x = 0.89855 \dots : x = 0.80739 \dots

Solve

x = 2.75535 \dots : x = 7.59196 \dots

x = 0.80739 \dots, x = 7.59196 \dots

Verify Solutions:

x = 0.80739 \dots

True

, x = 7.59196 \dots

True

The solutions are

x = 0.80739 \dots, x = 7.59196 \dots

x^{2} + 9 - x = 3

a, l = \frac{p}{4} + \frac{1}{4} \cdot p^{2} - 16 a

\frac{x ^{2}}{5 - 3 x ^{\frac{1}{5}} + 2} = 0

(8 - 4 x)^{2} = 2

(2 x - 1)^{\frac{1}{3}} - 3 = 0

What is the answer to (sqrt(x))/x+1+sqrt(x)+1/x = 17/4 ?
The answer to (sqrt(x))/x+1+sqrt(x)+1/x = 17/4 is x=0.80739…,x=7.59196…
Solve for x: (sqrt(x))/x+1+sqrt(x)+1/x = 17/4
The solution is x=0.80739…,x=7.59196…